Anti-arbitrage pricing system and method for subgraph data query based on tripartite game

Abstract

The invention provides an anti-arbitrage pricing system and method for subgraph data query based on a tripartite game, and relates to the technical field of data pricing, subgraph query and the tripartite game. The system comprises a seller used for uploading an original sub-graph to a pricing management platform for data transaction; the buyer is used for submitting the query graph to the pricing management platform, obtaining a corresponding result graph and paying the fee; the pricing management platform is used for publishing a transaction mechanism of each transaction cycle; pricing the original sub-graph of the seller; original sub-graphs uploaded by multiple sellers are integrated, and a global data graph and a view set are constructed; according to the query graph of the buyer, querying a result graph meeting the query graph from the view set, and pricing to complete data transaction; and recording the transaction data of each transaction cycle to optimize the transaction mechanism and platform parameters of the next transaction cycle. The objective of the invention is to solve the problem that an existing data transaction platform lacks a fine-grained query and pricing mechanism for graph data and has interest arbitrage risks.

Description

Technical Field

[0001] This invention relates to the fields of data pricing, subgraph querying, and three-party game theory, and particularly to an anti-arbitrage pricing system and method for subgraph data querying based on three-party game theory. Background Technology

[0002] With the rapid development of technologies such as big data, artificial intelligence, and knowledge graphs, graph data, as a data structure capable of efficiently representing entities and their complex relationships, has been widely used in numerous fields such as finance, healthcare, social networks, smart manufacturing, and the internet. Graph data not only intuitively describes the multidimensional relationships between entities but also supports complex relational reasoning and efficient subgraph queries, thus becoming an important foundation for data analysis and intelligent decision-making.

[0003] In the practical application and circulation of graph data, the demand for data trading is growing. Various enterprises and institutions hope to acquire or sell specific subsets of graph data (such as subgraphs, views, etc.) on demand through data marketplaces or data trading platforms to support their business innovation and intelligent analysis. However, existing data trading platforms primarily handle structured tabular or text data, lacking flexible, fine-grained subgraph-level query and pricing mechanisms for graph data. Especially in multi-party data trading scenarios, how to reasonably price subgraphs from different sources and with different values ​​has become a pressing technical challenge.

[0004] Furthermore, in the actual transaction ecosystem involving multiple sellers, platforms, and buyers, the three parties simultaneously exhibit game-theoretic dynamics and information asymmetry, posing additional challenges to subgraph queries and pricing of graph data. Firstly, the multi-party strategies and information asymmetry mean that the true quality, freshness, privacy-sensitive costs, and supply stability of sellers are difficult for platforms and buyers to fully observe, leading to a tendency for strategic reporting. Correspondingly, buyers' utility functions, budget limits, and tolerable privacy / SLA thresholds are privacy-sensitive, potentially allowing for "covert" optimization through query splitting / combination.

[0005] Currently, pricing technology for graph data queries is still immature. Traditional data pricing methods are difficult to apply directly to graph data, mainly due to the following reasons: (1) Graph data has a complex structure with high overlap and dependence between subgraphs, making it difficult to accurately assess the contribution of a single subgraph to the overall query results; (2) There is a lack of effective subgraph value assessment and allocation mechanisms, making it difficult to achieve fair and transparent pricing; (3) In actual transactions, buyers may obtain high-value data at low prices through multiple or combined queries, posing an arbitrage risk; (4) How to set up a model to maximize the interests of the platform, sellers, and buyers. To prevent the above-mentioned arbitrage behavior, some scholars have proposed anti-arbitrage pricing mechanisms based on concepts such as query result sensitivity and conflict sets, but these methods are mostly aimed at relational databases or simple data models and have not fully considered the structural characteristics and complexity of graph data. There is still a lack of systematic and effective technical solutions for query pricing and anti-arbitrage issues for graph data.

[0006] Therefore, there is an urgent need for a subgraph query and pricing method oriented towards graph data that supports multi-party participation, can accurately assess the contribution of subgraphs to query results, reasonably allocate data value, and has a mechanism to prevent arbitrage in order to promote the safe, compliant and efficient circulation of graph data. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention introduces a three-party game framework and constructs a multi-dimensional value assessment model to optimize anti-arbitrage pricing for graph data queries. It proposes an anti-arbitrage pricing system and method for sub-graph data queries based on three-party game theory, applicable to complex transaction scenarios with multiple sellers and buyers in the graph data market. This aims to solve the problems of existing data trading platforms lacking fine-grained query and pricing mechanisms for graph data and posing arbitrage risks. It achieves fair pricing, efficient querying, and secure circulation of graph data, meeting the multi-party graph data transaction needs of various scenarios such as financial risk control and medical collaboration.

[0008] On the one hand, this invention proposes an anti-arbitrage pricing system for subgraph data query based on three-party game theory. This system includes three types of participants in data transactions: sellers, buyers, and pricing management platforms.

[0009] The seller is used to upload its own original sub-graphs to the pricing management platform for data trading in accordance with the transaction mechanism published by the pricing management platform;

[0010] The buyer is responsible for submitting a query image to the pricing management platform based on the transaction mechanism published by the pricing management platform and the original sub-image uploaded by the seller; obtaining the result image provided by the pricing management platform based on the query image; and paying the fee for the result image.

[0011] The pricing management platform is used to publish the transaction mechanism for each transaction cycle; price the original subgraphs uploaded by sellers based on the transaction mechanism; integrate the original subgraphs from one or more sellers to generate a global data graph and construct a view set; receive query graphs uploaded by buyers and query the result graphs that satisfy the query graphs from the view set; price the result graphs based on the transaction mechanism; calculate the fees payable by the buyer and complete the data transaction according to the calculated fees; record the transaction data for each transaction cycle and use it to optimize the transaction mechanism and platform parameters for the next transaction cycle.

[0012] On the other hand, this invention proposes an anti-arbitrage pricing method for subgraph data query based on three-party game theory, which includes the following process:

[0013] The pricing management platform publishes the transaction mechanism and platform parameters for the current transaction cycle to all sellers and buyers;

[0014] Any seller After observing the aforementioned transaction mechanism, the seller's profit function is endogenously anticipated, and based on the principle of profit maximization, the seller... The decision is made to upload the original subgraph, and the data attribute set of the original subgraph is declared;

[0015] The pricing management platform sets a price for each original sub-image uploaded by the seller, based on the aforementioned transaction mechanism.

[0016] Using graph fusion and consistency verification algorithms, the pricing management platform integrates all the original subgraphs uploaded by sellers to generate a global data graph. and build view sets ;

[0017] Any buyer After observing the aforementioned transaction mechanism and all the original subgraphs uploaded by sellers, the buyer's utility function is endogenously predicted, and based on the principle of utility maximization, the buyer... The decision-maker submits the query graph to the pricing management platform and declares the data attribute set of the query graph;

[0018] Pricing management platform based on buyer Submitted query graph, from view set The query returns a combination of views that match the query graph as the result graph; at the same time, the corresponding set of sellers is obtained;

[0019] The pricing management platform prices the result graph according to the transaction mechanism, and the buyer makes the payment. Then, based on the pricing management platform's pricing of the original subgraph, the fee paid by the buyer is distributed to all sellers in the seller set, thus completing the data transaction.

[0020] After completing the data transactions for the current trading cycle, the trading mechanism and platform parameters for the next trading cycle are updated based on the dynamic strategy of Stackelberg game.

[0021] During each trading cycle, when the pricing management platform detects abnormal behavior, it adjusts the platform parameters in real time by triggering a fallback mechanism.

[0022] Furthermore, the trading mechanism includes: basic pricing rules, anti-arbitrage constraints, and view combination rules;

[0023] The specific content of the basic pricing rule is as follows: Any seller... The uploaded original sub-image is used as the sub-image to be priced. And based on the global data graph maintained in the pricing management platform during the current trading cycle. Calculate the subgraph to be priced using the subgraph contribution pricing rule. In the global data graph Shapley values ​​in the graph; using influence pricing rules, calculate the subgraph to be priced. The global data graph The fusion influence score is calculated; the calculated Shapley value and fusion influence score are normalized, and then the normalized Shapley value and fusion influence score are weighted and summed to obtain the subgraph to be priced. Pricing;

[0024] The specific content of the anti-arbitrage constraint is as follows: for any view to be priced... Define the view to be priced Conflict set A weighted set covering function is used to assign a base price to each salable base view in the pricing management platform; for any view to be priced... Find all sets of conflicts that can be covered from all base views. The basic view combination is used, and the price of each basic view combination is calculated according to the anti-arbitrage pricing function. The minimum calculated value is taken as the view to be priced. Pricing;

[0025] The specific content of the view combination rule is as follows: for any query vertex in the query graph... Construct query vertices candidate set The candidate set For view sets The set of all vertices in the set; query vertices based on pseudo-star isomorphism constraints. candidate set Perform filtering; add all filtered candidate view vertices to a queue, and then recursively prune the queue based on a ping-pong filtering strategy to obtain a refined candidate set;

[0026] Based on the refined candidate set, a candidate view containing all candidate view vertices in the refined candidate set is generated. Then, a view dependency graph is constructed by calculating the dependency strength between all candidate views. Based on a predefined priority criterion, the priority score of each candidate view in the view dependency graph is calculated, thereby generating the optimal view combination order of the query graph. A view-level dual-graph index is constructed to pre-store the connection relationship between vertices of each pair of candidate views in the global data graph.

[0027] Following the optimal view combination order of the query graph, all possible view combinations are recursively enumerated. During the recursive enumeration process, the view-level dual-graph index is used for verification. Based on the verification results, valid view combinations that are isomorphic to the query graph are retained. Then, the result graph of the query graph is generated based on the valid view combinations.

[0028] The platform parameters include: price vector Profit sharing ratio Privacy parameters Combined selection with view .

[0029] Furthermore, the subgraph contribution pricing rule is as follows: for the global data graph maintained in the pricing management platform during the current transaction cycle... Corresponding view set For this view set Perform random sampling to obtain Each sampling subset is used to calculate the impact of each sampling subset on the global data graph. The marginal contribution;

[0030] According to the sub-chart of the price to be determined The node overlap and edge connectivity between each sampling subset are considered in relation to the global data graph for each sampling subset. Assign a structural weight to the marginal contribution of each sample subset to the global data graph. The marginal contribution and the structural weights assigned to that marginal contribution are used to calculate the subgraph to be priced. In the global data graph Shapley value in;

[0031] The influence pricing rule is as follows: based on the influence propagation model, using the subgraph to be priced. As seed nodes, Monte Carlo simulation is used. The information propagation process is run once, and calculations are performed. The average number of nodes activated after each information propagation process is completed is used as the subgraph to be priced. The influence of dissemination; based on a structural indicator model, calculate the sub-graph to be priced. Structural indicators; pricing subplot The weighted sum of dissemination-related influence and structural indicators yields the sub-graph to be priced. The score for the integration influence.

[0032] Furthermore, the aforementioned any seller After observing the aforementioned transaction mechanism, the method for endogenously predicting the seller's revenue function is as follows: for any seller After observing the aforementioned transaction mechanism, the seller is determined. Seller decision variables The seller's decision variables This includes: supply Quality level Privacy cost parameters ; and the seller's decision variables It meets predefined capacity constraints, quality level constraints, quality constraints, and historical reputation score constraints;

[0033] Based on the aforementioned transaction mechanism, according to the seller Seller decision variables Define seller The seller's revenue function is expressed as:

[0034] ;

[0035] in Indicates the seller The benefits; Indicates an indicator function; For query graph Pricing; Indicates the seller Profit share; For the seller The cost function, , , and For the seller Cost coefficient;

[0036] The data attribute set of the original subgraph includes: quality level Freshness Privacy cost parameters .

[0037] Furthermore, the aforementioned any buyer After observing the aforementioned transaction mechanism and all the original subgraphs uploaded by sellers, the method for endogenously predicting the buyer's utility function is as follows: for any buyer After observing the aforementioned transaction mechanism and all the original subgraphs uploaded by the sellers, the buyer was determined. Buyer decision variables The buyer's decision variables Including: Purchase ratio Single query budget allocation Query the total budget multiple times and privacy tolerance ; and the buyer's decision variables It meets predefined constraints, including: total budget constraint, privacy compliance constraint, single query price constraint, and multi-query budget constraint;

[0038] Based on the aforementioned transaction mechanism, according to the buyer Buyer decision variables Define the buyer The buyer's utility function is:

[0039] ;

[0040] in Indicates buyer The utility; This represents the subjective utility weight of buyer j; To cover revenue; For privacy benefits; For quality assessment;

[0041] The data attribute set of the query graph includes: purchase ratio SLA level and privacy tolerance .

[0042] Furthermore, the pricing management platform uses the following method to price the result graph according to the transaction mechanism:

[0043] Based on the GFT pricing rules of the result graph, for the result graph Included Each of the smaller views has a custom view signal;

[0044] Resulting graph The Graph Laplace Matrix Spectral decomposition was performed to obtain the resulting graph. eigenvector matrix;

[0045] Based on the view signals and result diagrams of each sub-view The eigenvector matrix is ​​used to calculate the graph Fourier transform (GFT) coefficients for each small view.

[0046] Calculate the graph Fourier transform (GFT) coefficients of each mini-view. For the result image Spectral domain contribution;

[0047] Based on the spectral domain contribution of each subview, the base prices of all subviews are weighted and summed to obtain the resulting graph. Base pricing;

[0048] For the result image Perform sensitivity analysis and evaluate the results based on the preset indicators. To mitigate privacy risks, differential privacy theory is employed to set a privacy protection budget for the pricing management platform based on the risk assessment results. ;

[0049] Whether to trigger a perturbation is determined based on predefined multiple trigger conditions. If a perturbation is triggered, it is then determined based on a privacy protection budget. Choose a differential privacy noise mechanism, and then use the chosen differential privacy noise mechanism to modify the resulting image. Inject noise and update the result image. If no disturbance is triggered, the original result image is retained. ;

[0050] The current result graph is evaluated using multiple predefined quality indicators. Perform a data quality assessment and generate the current result graph based on the assessment results. Quality adjustment factor;

[0051] Based on a predefined privacy discount function, and according to the privacy protection budget Calculate the current result graph The strength of privacy protection;

[0052] View the current result image Quality adjustment factor, privacy protection strength and result graph The product of the base prices is used as the result graph. The pricing.

[0053] Furthermore, the specific details of determining whether to trigger a disturbance based on predefined multiple triggering conditions are as follows:

[0054] The result graph is processed according to predefined multiple trigger conditions. An evaluation is performed to obtain the evaluation results for each triggering condition;

[0055] The predefined multiple triggering conditions include: structural uniqueness check: result diagram The node's k-hop neighborhood signature uniqueness score exceeds 0.7; Node degree anomaly check: Result diagram Moderate degree or above The proportion of nodes exceeds 0.6; among them Standard deviation of degree for all nodes; Sensitive attribute check: Result plot Nodes with sensitive attributes exist; overlap check: result image The overlap with the query graph exceeds 80%;

[0056] Based on the GraphPerturbationDecider class, the resulting graph The results are obtained by weighted summation of all evaluation results. The risk score, when the risk score is >0.5 or the privacy protection budget... A perturbation is triggered when the value is less than 1.0.

[0057] Furthermore, the platform decision variables of the pricing management platform This includes: price vector Profit sharing ratio Privacy parameters View combination selection Profit Sharing ;

[0058] Based on the platform decision variables Define the platform objective function of the pricing management platform, including: maximizing social welfare or maximizing profit;

[0059] The maximization of social welfare is defined as follows:

[0060] ;

[0061] in Indicates buyer utility; Indicates the seller's profit; and has and ; This indicates the platform's operating costs;

[0062] The profit maximization is:

[0063] ;

[0064] in This represents the sum of prices for all buyer queries within the current trading period. This is a penalty item;

[0065] For any trading period, an alternating optimization strategy based on Stackelberg game is used to solve for the platform parameters of the next trading period.

[0066] Furthermore, the specific details of using an alternating optimization strategy based on Stackelberg game to solve for the platform parameters in the next trading cycle are as follows:

[0067] Initialize platform parameters, including: price vector Profit sharing ratio and privacy parameters And obtain the query graph provided by each buyer in the current transaction cycle. candidate view clusters ;

[0068] Retrieve platform parameters for the current trading period: Price Vector Profit sharing ratio Privacy parameters Combined selection with view ;

[0069] For each seller By maximizing the seller's revenue function, the seller's profit can be determined. The optimal response includes: shelf placement decision Supply and quality level ;

[0070] For each buyer By maximizing the buyer's utility function, the buyer's value can be determined. The optimal response; the buyer The optimal response is the purchase ratio. ;

[0071] Collect the best responses from all sellers and buyers, from arrive Execute the outer AO iteration loop, including the following process:

[0072] Fixed profit sharing ratio and privacy parameters The subgradient method is used to maximize the platform objective function, and price vector constraints and smoothing regularization constraints are applied to obtain the updated price vector. ;in This represents the number of iterations. This represents the maximum number of iterations.

[0073] In candidate view cluster The greedy algorithm is executed to obtain the updated view combination selection. ;

[0074] Fixed update price vector Combined selection with view Within a preset interval, the platform objective function is maximized using the projection gradient method, and L2 regularization constraints are applied to obtain the updated profit-sharing ratio. ;

[0075] Fixed update price vector View combination selection Profit sharing ratio Within a preset interval, updated privacy parameters are obtained by using line search or one-dimensional convex optimization. ;

[0076] Using the updated price vector View combination selection Profit sharing ratio and privacy parameters Calculate the optimal responses for all sellers and buyers, if the convergence condition is met or Then exit the loop and... , , and Used as a platform parameter for the next trading cycle; otherwise, the cycle continues.

[0077] The beneficial effects of adopting the above technical solution are as follows:

[0078] This invention uses a pricing management platform as its core, integrating sub-graphs uploaded by multiple sellers to construct a global data graph and view set. It supports buyers flexibly submitting query graphs to obtain result graphs and allows for the formation of a three-way game to achieve optimal benefits for all three parties. Specifically:

[0079] This invention supports efficient fusion of subgraphs uploaded by multiple sellers through multi-party subgraph fusion and consistency verification, automatically detects and resolves conflicts of nodes, edges, and attributes, and ensures the consistency of the global data graph structure.

[0080] This invention proposes a dynamic pricing strategy based on Stackelberg game theory. It introduces master-follower game theory, where the platform, as the leader, pre-determines the base price and trading rules. Each seller, as a follower, adjusts their data upload and pricing strategies accordingly to maximize profits. Before sellers upload their original subgraphs, the pricing management platform, as the leader, must first determine the base price and trading rules and publish the mechanism parameters for the current trading cycle. Each seller, as a follower, adjusts their data upload and pricing strategies based on these published parameters to maximize profits. This strategy constructs a Stackelberg three-party game model, forming a hierarchical decision-making and online stabilization linkage between the platform, sellers, and buyers.

[0081] This invention employs a weighted fusion of approximate Shapley values ​​and propagation / structural influence to comprehensively quantify the marginal value of a subgraph within the global graph, thus forming a pricing rule for subgraph contribution. Furthermore, this invention designs an anti-arbitrage pricing mechanism, using a pricing function based on conflict set theory that satisfies monotonicity and subadditivity, combined with a weighted set covering function, to prevent information arbitrage and bundled arbitrage.

[0082] This invention combines the VC algorithm with the GraphZero system to achieve efficient candidate filtering, combinatorial optimization and redundancy elimination under large-scale view sets, and supports isomorphic combination of complex query graphs.

[0083] This invention utilizes Graph Fourier Transform (GFT) to analyze the spectral energy contribution of each small view to the resulting graph, achieving a scientific pricing that balances structural and global perspectives. Furthermore, it introduces differential privacy protection, dynamically adjusting data prices based on noise injection intensity to achieve a balance between privacy protection and data value.

[0084] In summary, the method of this invention integrates subgraphs uploaded by multiple sellers through a platform to construct a global data graph and maintain diverse view sets, supporting flexible queries by buyers. It employs weighted pricing based on subgraph contribution, value assessment combining Shapley value and influence, a conflict set anti-arbitrage mechanism, and a privacy noise pricing mechanism to achieve fair, scientific pricing and secure circulation of graph data. Through a clear architectural design, standardized data preparation processes, and efficient view set management, it provides a foundation for multi-party data integration, flexible querying, and scientific pricing. This method can accurately assess the contribution of subgraphs to query results, rationally allocate data value, and possesses mechanisms to prevent arbitrage, thus promoting the secure, compliant, and efficient circulation of graph data. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of the architecture of the anti-arbitrage pricing system based on subgraph data query of three-party game theory in an embodiment of the present invention.

[0086] Figure 2 This is a flowchart of an anti-arbitrage pricing method for subgraph data query based on three-party game theory in an embodiment of the present invention;

[0087] Figure 3 This is a schematic diagram of the anti-arbitrage pricing mechanism in an embodiment of the present invention;

[0088] Figure 4 This is a flowchart illustrating the efficient view set query and combination process in an embodiment of the present invention;

[0089] Figure 5 This is a schematic diagram of the three-party game mechanism in an embodiment of the present invention. Detailed Implementation

[0090] To facilitate understanding of this application, specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. The following embodiments are illustrative of the invention but are not intended to limit its scope. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application.

[0091] Example 1:

[0092] Multi-party subgraph query and pricing arbitrage prevention scenarios for graph data, such as Figure 1 As shown, this embodiment proposes an anti-arbitrage pricing system for subgraph data query based on a three-party game framework. The system identifies three types of participating entities: sellers, pricing management platforms, and buyers. Sellers are responsible for uploading their own original subgraphs to the pricing management platform for data trading according to the transaction mechanism published by the pricing management platform.

[0093] The buyer is responsible for submitting a query graph to the pricing management platform based on the transaction mechanism published by the pricing management platform and the original sub-graph uploaded by the seller; obtaining the result graph provided by the pricing management platform based on the query graph; and paying the fee for the result graph.

[0094] The pricing management platform is used to publish the transaction mechanism for each transaction cycle; based on the transaction mechanism, it prices the original subgraphs uploaded by sellers; it integrates the original subgraphs from one or more sellers to generate a global data graph and construct a view set; it receives query graphs uploaded by buyers and retrieves the result graphs that satisfy the query graphs from the view set; it prices the result graphs based on the transaction mechanism; it calculates the fees payable by the buyer and completes the data transaction according to the calculated fees; it records the transaction data for each transaction cycle and uses it to optimize the transaction mechanism and platform parameters for the next transaction cycle.

[0095] This embodiment also performs preliminary data preparation by defining multiple graph data structures, enabling buyers and sellers to conduct data transactions with the pricing management platform. Specifically, the data structures include:

[0096] Global Data Graph The graph data set is generated by integrating all the original subgraphs uploaded by sellers and is maintained and dynamically updated by the pricing management platform.

[0097] Subgraph : The original sub-image uploaded by the seller.

[0098] view The tradable data segments in the pricing management platform, with each view corresponding to an original sub-graph uploaded by a seller.

[0099] Viewset A collection of tradable data fragments constructed and maintained by the pricing management platform, which serves as the object of transaction query for the pricing management platform.

[0100] Query Image The buyer converts the query request into a standard graph structure description that the pricing management platform can recognize, based on the query template provided and constrained in advance by the pricing management platform.

[0101] Result image The pricing management platform, based on the query graph... From view set The query retrieves a combination of views that match the query request.

[0102] In this embodiment, the pricing management platform integrates all subgraph data uploaded by sellers to form a unified and complete graph data set as a global data graph. The subset of the original image data uploaded by the seller will be used as the sub-image. This represents the portion of the graph structure owned by the seller. The set of views maintained by the pricing management platform is considered as a view set. And the view This represents a view set. A small view within the pricing management platform represents different data segments available for trading. The pricing management platform provides buyers with query templates, structure validation, and visual design tools, allowing buyers to submit query requests based on their business needs. These queries are typically described using graph structures (such as subgraph patterns, paths, structural constraints, etc.). The result graph represents the pricing management platform's response based on the query graph. In view set Execute query operations and map them to the global data graph. The actual data subplot is returned to the buyer.

[0103] Example 2:

[0104] To verify the applicability and performance of this embodiment in a real-world environment, the experimental data used in this embodiment can be derived from the following categories: publicly available graph datasets commonly used in academia, such as social networks (e.g., Facebook, Twitter), citation networks (e.g., Cora, Citeseer), and knowledge graphs (e.g., DBpedia, YAGO). These datasets have clear structures and moderate sizes, facilitating algorithm verification and comparative experiments. Graph generation algorithms (e.g., Barabási–Albert, Erdős–Rényi) are used to synthesize graph data with different structural features, simulating real-world scenarios where multiple parties possess different subgraphs, facilitating the testing of the system's versatility and robustness. With authorization, actual business graph data within enterprises (e.g., financial transaction networks, supply chain networks, etc.) can be collected.

[0105] This embodiment presents an anti-arbitrage pricing method for subgraph data query based on three-party game theory, such as... Figure 2 As shown, the anti-arbitrage pricing system based on subgraph data query of three-party game theory, as described in Example 1, is implemented. The method includes the following steps:

[0106] The pricing management platform publishes the transaction mechanism and platform parameters for the current transaction cycle to all sellers and buyers.

[0107] The trading mechanism includes: basic pricing rules, anti-arbitrage constraints, and view combination rules.

[0108] The specific content of the basic pricing rule is as follows: Any seller... The uploaded original sub-image is used as the sub-image to be priced. And based on the global data graph maintained in the pricing management platform during the current trading cycle. Calculate the subgraph to be priced using the subgraph contribution pricing rule. In the global data graph Shapley values ​​in the graph; using influence pricing rules, calculate the subgraph to be priced. The global data graph The fusion influence score is calculated; the calculated Shapley value and fusion influence score are normalized, and then the normalized Shapley value and fusion influence score are weighted and summed to obtain the subgraph to be priced. The pricing.

[0109] (1)

[0110] in Represents the subgraph to be priced In the global data graph Shapley value in; For global data graph The corresponding view set; This represents the sampling reference set, i.e., the view set that does not contain the subgraph to be priced, a; A subset of the view set; For subset Global data graph The value function value used in this embodiment is: number of covered nodes, number of edges, structural integrity, etc. For in subset Add a subgraph to be priced Then, the global data graph The value function value. Since the exact calculation of formula (1) is extremely complex, this embodiment uses a sampling method to approximate the Shapley value in order to quantify the subgraph to be priced. Global data graph The marginal contribution.

[0111] The subgraph contribution pricing rule is as follows: for the global data graph maintained in the pricing management platform during the current trading cycle... Corresponding view set For this view set Perform random sampling to obtain Each sampling subset is used to calculate the impact of each sampling subset on the global data graph. The marginal contribution.

[0112] (2)

[0113] in Indicates the first a sampling subset, and ; express Global data graph The marginal contribution.

[0114] At this point, the subgraph to be priced will be... In the global data graph Approximate Shapley value in Represented as:

[0115] (3)

[0116] According to the sub-chart of the price to be determined The node overlap and edge connectivity between each sampling subset are considered in relation to the global data graph for each sampling subset. The marginal contribution is assigned a structural weight.

[0117] (4)

[0118] in Represented as a sampling subset Global data graph The structural weights of the marginal contribution allocation are used to reflect and The structural relationship, and the structural weight can be obtained by weighting the node overlap and edge connectivity; Represents the subgraph to be priced The set of nodes; Represents a sample subset The set of nodes; Represents the subgraph to be priced The set of edges; Represents a sample subset The set of edges; and All are weighting coefficients.

[0119] Based on each sampling subset, the global data graph The marginal contribution and the structural weights assigned to that marginal contribution are used to calculate the subgraph to be priced. In the global data graph The Shapley value in [the context].

[0120] (5)

[0121] In this embodiment, the pricing management platform records and manages the weighted Shapley value of each subgraph as its contribution, and supports dynamic adjustment of parameters to adapt to pricing needs in different business scenarios. Through the above process, the platform can efficiently and scientifically quantify and price the contribution of subgraphs, ensuring the fairness and transparency of multi-party data transactions.

[0122] In practical pricing scenarios, focusing solely on dissemination effects or structural position often fails to comprehensively measure the true value of nodes or subgraphs. Therefore, integrating dissemination-based influence and structural indicators becomes a more scientific and reasonable pricing method. By weighting and fusing influence calculated based on a dissemination model with structural indicators, both the node's diffusion capacity and its key position within the network are considered. The pricing management platform quantifies the subgraphs to be priced as information sources within the network. The overall influence on the market is used as one of the indicators for pricing.

[0123] The influence pricing rule is as follows: based on the influence propagation model, using the subgraph to be priced. As seed nodes, Monte Carlo simulation is used. The information propagation process occurs in each run; in each run information propagation process, starting from the seed node, in the global data graph... Random propagation is performed, and the number of activated nodes after each propagation process is counted. Calculation The average number of activated nodes after the end of each information propagation process is used as the subgraph to be priced. The influence of dissemination.

[0124] This embodiment uses the influence propagation model to evaluate its diffusion ability in the network, represented as:

[0125] (6)

[0126] in Represents the subgraph to be priced The influence of communication; This represents the average number of activated nodes after the Monte Carlo simulation. Represents a subgraph to be priced The expected number of nodes that will eventually be activated during the random propagation process, which is the set of seed nodes, representing the information source.

[0127] Based on the structural indicator model, calculate the subgraph to be priced. The structural indicators. This embodiment uses the PageRank algorithm to evaluate the subgraph to be priced. Its position in the network structure is represented as:

[0128] (7)

[0129] in Represents the subgraph to be priced Structural indicators; Represents the subgraph to be priced PageRank value; This represents the damping coefficient, which is typically taken as 0.85. Represents a global data graph The total number of nodes in; Represents the subgraph to be priced Any node; Represents a node PageRank value; Represents a node The degree of departure.

[0130] Treatment of pricing subgraph The weighted sum of dissemination-related influence and structural indicators yields the sub-graph to be priced. The score for the integration influence.

[0131] (8)

[0132] in Represents the subgraph to be priced The score of integration influence; These are the weighting coefficients. It can be adjusted according to actual business needs. The larger the scale, the more emphasis is placed on actual dissemination capabilities, such as advertising and virus spread. The smaller the scale, the more emphasis is placed on structural position, such as in scenarios like cybersecurity and public opinion monitoring.

[0133] Based on this, by normalizing the calculated Shapley value and fusion influence score, and then by weighted summing the normalized Shapley value and fusion influence score, the target subgraph is obtained. The pricing.

[0134] (9)

[0135] in Represents the subgraph to be priced Pricing; The weights are merged and normalized.

[0136] In data pricing platforms, to prevent buyers from arbitrage through multiple low-price combination queries, the platform needs to introduce an anti-arbitrage mechanism. The core approach is pricing based on conflict sets: a conflict set refers to the set of all views that are inconsistent with the current query results but are involved in the query process. A larger conflict set indicates that the query excludes more possible view instances, revealing more information, and therefore the price should be higher. To prevent information arbitrage and bundled arbitrage, a pricing function that satisfies monotonicity (the larger the conflict set, the higher the price) and subadditivity (the price of a joint query does not exceed the sum of the prices of individual queries) needs to be designed to ensure that the query price matches its information exclusion capability. Ultimately, the platform applies a pricing function that satisfies the above properties to the conflict set and employs specific pricing methods such as weighted set covering functions to achieve fair and arbitrage-free data pricing.

[0137] The specific content of the anti-arbitrage constraint is as follows: for any view to be priced... Define the view to be priced Conflict set It should be noted that in this embodiment, subgraphs and views are treated as the same graph structure data; the difference in naming is solely for business perspective: the former refers to the original data provided by the seller, while the latter refers to the final form provided to the buyer. Therefore, the subgraph to be priced... and Pricing View These are actually two representations of the same graph structure data, and their pricing is essentially the same. For example... Figure 3 As shown, regarding the inquiry provided by the buyer And according to the query Query results , construct query After obtaining the results The conflict set of the time.

[0138] (10)

[0139] in For query After obtaining the results The conflict set at time; C represents the query The candidate set; This represents the view set used during the query process; Indicates in Execute query The results obtained quantify how many possible database instances the query actually excluded by calculating the size and range of the conflict set, thus measuring the amount of information revealed by the query.

[0140] The view set of all salable basic views in the pricing management platform is denoted as... A weighted set coverage function is used to assign a base price to each base view; where The number of base views.

[0141] For any view to be priced From view set Find all sets of conflicts that can be covered. The basic view combination is used, and the price of each basic view combination is calculated according to the anti-arbitrage pricing function, with the minimum value being used as the view to be priced. The pricing.

[0142] (11)

[0143] in View for pricing Pricing; A pricing function that satisfies monotonicity and subadditivity; Basic View The base price; The index set of the base view; Basic View The set of conflicts.

[0144] The pricing function that satisfies monotonicity and subadditivity Represented as:

[0145] (12)

[0146] in Indicates query In the results The price is set below. To avoid information arbitrage, the pricing function... It must satisfy monotonicity, that is: if the query The information revealed is for querying The subset of information revealed, namely Derivable Then query The price must not exceed the price quoted. The price is determined by formula (12). The final price can be mapped using formula (12), enabling arbitrage-free data pricing. This ensures that regardless of how the buyer combines purchases, they cannot obtain more information at a total price lower than the platform's pricing, thus eliminating information arbitrage and bundled arbitrage, and protecting the interests of both the platform and the seller.

[0147] In viewset query scenarios, the goal is to retrieve data from the viewset. This method selects and combines several smaller views to ensure their overall structure is isomorphic to a given query graph. For view set query scenarios, this embodiment proposes combining the VC algorithm with the GraphZero system to efficiently select, combine, and validate smaller views in a view set in stages, ensuring their overall structure is isomorphic to the given query graph. This fully leverages the advantages of both algorithms in candidate selection, combination optimization, and redundancy elimination, achieving efficient and accurate view combination queries. Through multiple optimizations, including local structure compatibility preprocessing, dependency pruning, optimal combination order generation, index acceleration, and redundancy elimination, the efficiency and accuracy of combination queries under large-scale view sets are significantly improved.

[0148] The specific content of the view combination rule is as follows: for any query vertex in the query graph... Construct query vertices candidate set The candidate set For view sets The set of all vertices in the set; query vertices based on pseudostar isomorphism constraints (PSIC). candidate set Filtering is performed. Specifically, this includes:

[0149] View sets maintained by the pricing management platform As a set of candidate views for the query graph.

[0150] For any query vertex in the query graph According to the query vertex Labels of all queried neighbor vertices For querying vertices Group all queried neighbor vertices to obtain the queried vertex. All Neighbor Label Equivalence Class .

[0151] Based on query vertex All Neighbor Label Equivalence Class By checking the candidate set in sequence Does the 1-hop neighborhood of each candidate view vertex satisfy the PSIC constraint for the candidate set? Perform vertex-level filtering to remove candidate view vertices that do not satisfy the PSIC constraints from the candidate set. .

[0152] The PSIC constraint is: for each neighbor label equivalence class equivalence class of the neighbor label Arrange all queried neighbor vertices in any order, and select the top vertices in that arrangement. Each queried neighbor vertex constitutes a subset of vertices. ;in , This represents any permutation of the equivalence classes of neighbor labels.

[0153] Based on the vertex subset For candidate set Any candidate view vertex in If the candidate view vertex If any of the following conditions are not met, then the candidate view vertex will be... From the candidate set Removed from the middle.

[0154] Non-empty intersection condition: for a subset of vertices Any query neighbor vertex in Candidate view vertices 1-hop neighbor set With candidate set The intersection of them is not empty.

[0155] (13)

[0156] Size constraint: Vertex subset The number of vertices does not exceed the number of candidate view vertices Neighbor set and candidate set The number of vertices in the union set.

[0157] (14)

[0158] in It is a subset Query the number of neighboring vertices. Candidate view vertex The number of vertices in the union of the neighbor set and the candidate set.

[0159] After performing vertex-level filtering on the candidate set of all query vertices in the query graph, if the view set If none of the nodes in any view exist in the candidate set of any query vertex, then that view is removed from the candidate view set. Further view-level filtering is then performed; if none of the vertices in a view can serve as candidate view vertices for any query vertex, then the entire view is discarded.

[0160] (15)

[0161] All filtered candidate view vertices are added to a queue, and then the queue is recursively pruned based on a ping-pong filtering strategy to obtain a refined candidate set.

[0162] In this embodiment, a ping-pong filtering strategy is employed to recursively prune redundant candidate views due to dependency failures, further narrowing the candidate space and ensuring that only views compatible with the local structure of the query graph are retained. All view vertices filtered by PSIC (i.e., the candidate set is cleared or the vertices are removed) are added to a queue (Queue), and a breadth-first search (BFS) is recursively used to prune the queue. This involves traversing each candidate view vertex in the queue. For candidate view vertices any neighboring vertex If neighboring vertices Neighbor set and candidate view vertices The corresponding candidate set of query vertices If the intersection of the two vertices is empty, then the neighboring vertices will be... From neighboring vertices The corresponding candidate set of query vertices Removed from the middle, represented as:

[0163] (16)

[0164] in yes The corresponding query vertex; yes The corresponding query vertex.

[0165] Based on the refined candidate set, a candidate view containing all candidate view vertices in the refined candidate set is generated. Then, a view dependency graph is constructed by calculating the dependency strength between all candidate views. Based on a predefined priority criterion, the priority score of each candidate view in the view dependency graph is calculated, thereby generating the optimal view combination order of the query graph.

[0166] Based on predefined priority criteria, the coreness, connection density, number of candidates, and price of each view are calculated to reflect its coreness in the dependency graph and its closeness with other views. This generates the optimal view combination order, prioritizing views with close dependencies, few candidates, and low prices to prune ineffective combination paths in advance to the maximum extent possible.

[0167] Construct a view-level bi-graph index to pre-store the connection relationships of vertices in the global data graph between each pair of candidate views.

[0168] To accelerate combinatorial validation, this embodiment constructs a view-level bigraph index for pre-storing the connectivity relationships of vertices between each pair of candidate views in the global data graph. This index supports... Cross-view vertex connectivity queries with time complexity significantly improve the efficiency of combinatorial validation.

[0169] Following the optimal view combination order of the query graph, all possible view combinations are recursively enumerated. During the recursive enumeration process, the view-level dual-graph index is used for verification. Based on the verification results, valid view combinations that are isomorphic to the query graph are retained, and then the result graph of the query graph is generated based on the valid view combinations.

[0170] Each time a new view is added, the dual-graph index is used to quickly verify whether its edge relationship with the selected views matches the query. Figure 1 If a new view is incompatible with existing combinations in terms of structure, labels, or edge relationships, it is immediately pruned, terminating the combination path and retaining only all valid combinations isomorphic to the query graph. These combinations can be stitched together to reconstruct a result graph isomorphic to the query graph. The results are then sorted, deduplicated, or priced according to business needs, ultimately providing users with efficient and accurate query results.

[0171] In this embodiment, a two-stage Stackelberg game model is used to divide the data transaction process into two stages: Stage 1 (Platform Mechanism Design): The platform, as the leader, first announces its pricing strategy, i.e., platform parameters, such as the base price vector, profit-sharing ratio, differential privacy strength, and view combination selection. Stage 2 (Follower Response): The seller set S and the buyer set M, as followers, observe the platform strategy and simultaneously make optimal responses. The platform intrinsically anticipates the follower response function during the design phase. and And the equilibrium is solved by optimizing the problem.

[0172] Any seller After observing the aforementioned transaction mechanism, the seller's profit function is endogenously anticipated, and based on the principle of profit maximization, the seller... The decision is made to upload the original subgraph and to declare the data attribute set of the original subgraph.

[0173] The arbitrary seller After observing the aforementioned transaction mechanism, the method for endogenously predicting the seller's revenue function is as follows:

[0174] Any seller After observing the aforementioned transaction mechanism, the seller is determined. Seller decision variables The seller's decision variables This includes: supply Quality level Privacy cost parameters .

[0175] The seller's decision variables The following constraints must be met: capacity constraints Quality level constraints Quality constraints and historical credit score constraints ;in For the seller Maximum capacity limits, such as storage or computing resource limitations; For the seller Optional set of quality levels Or a range of values; Indicates quality requirements; The minimum quality threshold set for the pricing management platform; For the seller Historical reputation scores, such as those based on transaction success rates or buyer feedback; A reputation threshold set for the pricing management platform.

[0176] Based on the aforementioned transaction mechanism, according to the seller Seller decision variables Define seller The seller's revenue function is expressed as:

[0177] (17)

[0178] in Indicates the seller The benefits; Indicates the indicator function, if the seller participate If the combination is true, the value is 1; otherwise, the value is 0, used to filter out query graphs that did not participate. ; For query graph The pricing is the transaction price calculated by the pricing management platform based on the anti-arbitrage framework; Indicates the seller The profit share, i.e., the seller's revenue distribution ratio in the query chart. , It is the profit-sharing weight set by the pricing management platform (which affects incentives); It represents the seller's contribution weight to the query graph, determined based on the Shapley value or influence metric. For the seller Cost, cost function Designed as a convex function, and having To ensure that the return function is concave; where , and For the seller The cost coefficient; to ensure that the equilibrium can be solved, the seller's revenue function is designed as a concave function.

[0179] The data attribute set of the original subgraph includes: quality level Freshness Privacy cost parameters .

[0180] In this embodiment, each seller After observing the transaction mechanism published by the pricing management platform, a decision is made on whether to upload the original subgraph. and the quality level of the upload Freshness Privacy cost parameters In order to maximize their own utility. Specifically, the seller weighs the profit-sharing ratio. and base price To make a decision, if the platform is set... higher or This is advantageous, as sellers are more inclined to upload high-quality sub-images. The platform adjusts in real-time: it monitors seller responses and can dynamically fine-tune θ or p to incentivize participation and ensure the view set is optimized. The richness of the content means that enough sellers upload high-quality sub-images. The specific implementation of the platform's dynamic fine-tuning is divided into three steps: "triggering conditions, adjustment strategies, and stopping criteria". Fine-tuning needs to continue until "core indicators meet the standards and are stable".

[0181] Using graph fusion and consistency verification algorithms, the pricing management platform integrates all the original subgraphs uploaded by sellers to generate a global data graph. and build view sets The specific content is as follows:

[0182] In this embodiment, when the pricing management platform purchases the sub-image to be priced uploaded by the seller... Next, it needs to be integrated with the existing global data graph. The platform will perform fusion. To this end, it will employ graph fusion and consistency verification algorithms to detect... and The system checks for ID conflicts, inconsistent attributes, or duplicate relationships among nodes and edges, and handles these issues according to a pre-defined conflict resolution strategy to ensure that the merged graph structure is complete and meets the platform's consistency constraints.

[0183] In this embodiment, after the fusion is completed, the platform will also base the pricing subgraph on the subgraph to be priced. The multidimensional structural features, including but not limited to: basic topology, global features, spectral features, and semantic features, are used to determine the pricing subset graph. Build an efficient tag inverted index to facilitate subsequent view matching, querying, and pricing. The process of building a tag inverted index can be summarized as follows: data extraction, traversing subgraphs, and extracting structural features; index construction, establishing a mapping between label and subgraph IDs; composite index, pre-computing common label combinations; persistence, saving to storage such as Elasticsearch; optimization: compression, tiering, and caching.

[0184] The subgraph to be priced Add to the view set maintained by the pricing management platform during the current trading period. Simultaneously update the sub-graph with the price to be determined. and the merged global data graph The relevant management information is used to complete the warehousing process for the sub-images to be priced.

[0185] The entire process not only ensures data integrity and consistency, but also allows the platform to synchronously update relevant metadata, version information, and access permissions. This ensures that newly added graphs can be seamlessly integrated with the overall database system, enabling efficient data management and utilization. Through metadata and access control, seamless integration and efficient utilization of new data with the platform's database are achieved.

[0186] Any buyer After observing the aforementioned transaction mechanism and all the original subgraphs uploaded by sellers, the buyer's utility function is endogenously predicted, and based on the principle of utility maximization, the buyer... The decision is to submit the query graph to the pricing management platform and declare the data attribute set of the query graph.

[0187] any buyer After observing the aforementioned transaction mechanism and all the original subgraphs uploaded by sellers, the method for endogenously predicting the buyer's utility function is as follows:

[0188] Any buyer After observing the aforementioned transaction mechanism and all the original subgraphs uploaded by the sellers, the buyer was determined. Buyer decision variables The buyer's decision variables Including: Purchase ratio Single query budget allocation Query the total budget multiple times and privacy tolerance ; and the buyer's decision variables Satisfy predefined constraints, including: total budget constraint Privacy compliance constraints Single query price constraint and multi-query budget constraints ;in Allocate the sum to the budget; For privacy parameters; For the buyer The submitted query graph.

[0189] Based on the aforementioned transaction mechanism, according to the buyer Buyer decision variables Define the buyer The buyer's utility function is:

[0190] (18)

[0191] in Indicates buyer The utility; This represents the subjective utility weight of buyer j, used to reflect the importance of the query to the buyer, and is calibrated by the buyer's business needs or the platform based on historical behavior; To cover revenue, and have , It is a scaling factor used to control the magnitude of coverage gains; To control the growth rate of covered returns, this is used to represent the impact of the purchase ratio on returns; For privacy benefits, and there are , This is the privacy discount strength coefficient, used to control the magnitude of the impact of the level of privacy protection on utility; The decay coefficient controls the exponential decay rate of privacy benefits; For quality assessment, and have ; , and The concavity was verified using the second derivative. and To ensure that the equilibrium can be solved, the buyer's utility function is designed as a concave function.

[0192] The data attribute set of the query graph includes: purchase ratio SLA level and privacy tolerance .

[0193] In this embodiment, the buyer After observing the platform mechanism and the sub-atlas uploaded by the seller, submit a query graph. And decision query graph Purchase ratio SLA level and privacy tolerance To maximize net utility, buyers adjust their queries based on price sensitivity and privacy requirements, using a lookup table provided by the platform. After collecting buyer responses, the platform assesses market demand based on buyer feedback for subsequent mechanism optimization.

[0194] Pricing management platform based on buyer Submitted query graph, from view set The query returns a combination of views that match the query graph as the result graph; at the same time, it retrieves the set of sellers corresponding to the result graph.

[0195] like Figure 4 As shown, after completing data integration and view set management, the platform provides the buyer with flexible query interfaces and a secure data access environment. Based on business needs, the buyer designs query graphs using the query templates provided by the platform, clarifying the structure and constraints. The buyer then submits the query graphs to the platform according to its own requirements. The platform in the view set Search and query graph Related small views are used to generate result images that meet the query conditions through splicing, combination, and other methods. .

[0196] The pricing management platform prices the resulting graph according to the transaction mechanism, and the buyer makes the payment. Then, based on the pricing management platform's pricing of the original subgraph, the fee paid by the buyer is distributed to all sellers in the seller set, thus completing the data transaction.

[0197] In the context of pricing data based on graphs, the platform generates a result graph by stitching together multiple smaller views. To ensure fair and scientific pricing, it is necessary to quantify the impact of each small view. The graph Fourier Transform (GFT) provides a spectral domain analysis tool for this purpose: by projecting the graph signal onto the graph Laplace feature space, it is possible to capture structural changes and global features. This embodiment, based on GFT, proposes a weighted pricing method based on spectral contribution. This method quantifies the energy contribution of each small view in the resulting graph's spectral domain, achieving a precise measurement of structural and global information. Based on this, it weights the prices of each small view according to its contribution, ultimately arriving at a reasonable pricing for the resulting graph. That is, each small view contributes to the overall structure and information of the resulting graph. Price contribution and its The energy overlap in the GFT spectral domain is proportional to the energy overlap.

[0198] Based on the GFT pricing rules of the result graph, for the result graph Included Each of the smaller views has a custom view signal.

[0199] In this embodiment, the input to the GFT pricing rule of the result graph is the result graph. , the result image The node set in the is denoted as The edge set is denoted as The weight matrix is ​​denoted as Resulting image Depend on It is composed of several small views pieced together. And the base price for each small view is denoted as For each small view In the result image Define view signals .

[0200] (19)

[0201] in For the result image The node.

[0202] Resulting graph The Graph Laplace Matrix Spectral decomposition was performed to obtain the resulting graph. The eigenvector matrix.

[0203] In this embodiment, the resulting diagram is constructed. degree matrix , is represented as:

[0204] (20)

[0205] in For the result image The nodes; and then construct the Laplace matrix:

[0206] (twenty one)

[0207] Through the Perform spectral decomposition, find eigenvalues ​​and eigenvectors, and obtain the resulting graph. The eigenvector matrix of is represented as:

[0208] (twenty two)

[0209] in It is the eigenvalue matrix; The eigenvector matrix, , For the result image The total number of nodes in the graph. The eigenvector matrix provides an orthogonal basis for the subsequent graph Fourier transform.

[0210] Based on the view signals and result diagrams of each sub-view Given the eigenvector matrix, calculate the graph Fourier transform (GFT) coefficients for each small view, expressed as:

[0211] (twenty three)

[0212] in yes Representation in the spectral domain.

[0213] Calculate the graph Fourier transform (GFT) coefficients of each mini-view. For the result image Spectral domain contribution.

[0214] In this embodiment, the energy proportion method is used to calculate the sum of squares (energy) of the GFT spectral coefficients and normalize it with the sum of the energies of all small views to obtain the spectral domain energy proportion of each small view to the resulting image. This proportion quantifies the actual contribution of the small view to the structure and information of the resulting image, and is expressed as:

[0215] (twenty four)

[0216] in , Indicates the first Each feature value.

[0217] Based on the spectral domain contribution of each subview, the base prices of all subviews are weighted and summed to obtain the resulting graph. Basic pricing .

[0218] (25)

[0219] In other words, the price contribution of each subview is equal to its base price multiplied by its energy percentage, and the sum of the weighted prices of all subviews is the total price of the resulting graph. This pricing method can scientifically reflect the structural and global value of each subview in the resulting graph, achieving fair and arbitrage-free data pricing.

[0220] In this embodiment, privacy noise pricing aims to protect data privacy while scientifically and reasonably adjusting the price of graph data. By assessing the privacy risks of the resulting graph, setting differential privacy parameters, injecting noise of appropriate intensity, evaluating data quality loss, and finally adjusting the price with a discount based on the strength of privacy protection, a balance between privacy protection and data value is achieved.

[0221] For the result image Perform sensitivity analysis and evaluate the results based on the preset indicators. To mitigate privacy risks, differential privacy theory is employed to set a privacy protection budget for the pricing management platform based on the risk assessment results. .

[0222] In this embodiment, preset indicators are used to evaluate the sensitivity of information such as nodes, edges, and attributes in the graph. These preset indicators include, but are not limited to, structural complexity, overlap with the original data, and the uniqueness of nodes or edges, among others, to comprehensively assess the privacy risks of the graph data. Based on this, differential privacy theory is employed to set privacy protection parameters. .in, The smaller the value, the stronger the privacy protection, but the availability and accuracy of the data will also decrease accordingly.

[0223] Whether to trigger a perturbation is determined based on predefined multiple trigger conditions. If a perturbation is triggered, it is then determined based on a privacy protection budget. Choose a differential privacy noise mechanism, and then use the chosen differential privacy noise mechanism to modify the resulting image. Inject noise and update the result image. If no disturbance is triggered, the original result image is retained. .

[0224] In this embodiment, noise injection is a closed-loop process: a differential privacy noise mechanism is selected based on the ϵ value, perturbations are triggered under multiple conditions, targeted operations are performed, and pricing, support, and improvements are optimized using quality assessment results. In the above process, graph perturbation is not always necessary; triggering is determined through multi-condition evaluation. Predefined multi-trigger conditions include: structural uniqueness check: node k-hop neighborhood signature uniqueness score > 0.7; node degree anomaly check: the proportion of nodes with a degree exceeding 3σ (σ is the standard deviation of all node degrees) > 0.6; sensitive attribute check: presence of attributes such as SSN and salary; and overlap with the original graph check: overlap rate > 0.8. Value check: Forced perturbation is applied when the overall score is less than 1.0. These conditions are used to calculate a risk score using the GraphPerturbationDecider class, and the score is adjusted when the overall score is greater than 0.5 or less. Perturbation is triggered when the value is <1.0. Once triggered, the system performs targeted operations, including: edge perturbation: randomly adding / deleting edges, the number of which is controlled by Laplace noise, changing a maximum of 20% of the edges; adding spurious edges based on the k-degree anonymization idea to smooth the degree distribution; attribute perturbation: adding Laplace noise to numerical attributes, and generalizing categorical attributes using random responses; and adding spurious nodes: adding ≤10% spurious nodes to increase the difficulty for attackers to identify them. These operations are executed by the GraphPerturbationExecutor class and detailed logs are recorded for auditing to ensure process traceability.

[0225] The choice of differential privacy noise mechanism directly depends on the size of the privacy budget. A smaller value indicates a stricter privacy protection requirement. Common differential privacy noise mechanisms include the Laplace mechanism and the exponential mechanism. Depending on the specific needs, nodes, edges, or attributes of the graph can be perturbed, such as randomly adding or deleting edges or modifying node attributes. The selection process for the differential privacy noise mechanism is implemented through an automated decision tree, including the following cases: strong privacy protection. It employs a Gaussian noise mechanism to provide differential privacy guarantees. Suitable for highly sensitive scenarios such as healthcare and finance, but may reduce data availability. Medium privacy protection. The selection mechanism is based on the query type: Numeric queries (such as count / sum) use the Laplace Mechanism, with a noise scale of [missing information]. Edge-difference privacy is used for edge-difference queries; discrete selection queries use an exponential mechanism. This approach balances privacy and utility and is suitable for general business data. (Weak privacy protection) : Using Laplace noise or randomized response mechanism, the true response probability Prioritize data availability; suitable for public or low-sensitivity data. This selection is performed automatically through the NoiseMechanismSelector class, ensuring the mechanism matches the query type and sensitivity.

[0226] The current result graph is evaluated using multiple predefined quality indicators. Perform a data quality assessment and generate the current result graph based on the assessment results. The quality adjustment factor.

[0227] Quality metrics include: structural similarity (based on graph edit distance, ranging from 0 to 1), edge retention rate (the proportion of original edges retained), degree distribution similarity (calculated using KL divergence), attribute accuracy (numerical error <10% is considered accurate), and overall utility score (weighted score, ranging from 0 to 1). These metrics are calculated by the DataQualityEvaluator class and comprehensively reflect data usability.

[0228] The assessment results directly drive dynamic pricing, i.e., final price = base price × privacy discount. × Quality adjustment factor (utility score), where the privacy discount increases as ϵ decreases, such as At a utility score of 0.1, the discount reaches 66%. The quality adjustment factor decreases as the utility score decreases, with an additional discount of 10-30% when the utility score is <0.5. Simultaneously, user-friendly reports are generated, such as "Utility score 0.85, suitable for machine learning," supporting informed decision-making; and guiding adaptive optimization, such as suggesting increasing the utility score when it is <0.7. Verify SLA compliance, such as a utility score ≥ 0.65; and continuously improve the mechanism by comparing perturbation strategies through A / B testing.

[0229] Based on a predefined privacy discount function, and according to the privacy protection budget Calculate the current result graph The strength of privacy protection;

[0230] In this embodiment, the design follows Increased privacy discount function Common forms include:

[0231] (26)

[0232] in It is an adjustment parameter related to the privacy discount strength coefficient; The parameter is the attenuation coefficient.

[0233] View the current result image Quality adjustment factor, privacy protection strength and result graph The product of the base prices is used as the result graph. The pricing strategy aims to achieve a dynamic balance between privacy protection and data value, expressed as:

[0234] (27)

[0235] in This is the quality adjustment factor, and the result is shown in the graph. The higher the quality, the higher the utility score.

[0236] Thus, the stronger the privacy protection (i.e.) The smaller the value (the smaller the value), the larger the price discount, and the lower the final price, achieving a balance between privacy protection and data value. Output: the resulting graph g after injecting noise and its final price. Users can obtain data that meets privacy protection requirements, and the platform can set reasonable prices based on the strength of privacy protection and data quality, balancing data security and commercial value.

[0237] Existing technologies lack formal analysis of the stability of the interaction among the three parties, leading to market inefficiency and increased arbitrage risk. This embodiment, through the Stackelberg game framework, provides equilibrium existence determination, numerical solution, and fallback mechanism to ensure the stable operation of the market under privacy protection and no arbitrage constraints, thus solving the equilibrium problem of the dynamic game among the platform, sellers, and buyers in graph data trading.

[0238] After completing the data transactions for the current trading cycle, the trading mechanism and platform parameters for the next trading cycle are updated based on the dynamic strategy of Stackelberg game.

[0239] Platform decision variables of pricing management platform This includes: price vector Profit sharing ratio Privacy parameters View combination selection Profit Sharing .

[0240] Based on the platform decision variables Define the platform objective function of the pricing management platform, including: maximizing social welfare or maximizing profit; wherein maximizing social welfare is:

[0241] (28)

[0242] in Indicates buyer utility; Indicates the seller's profit; This represents the platform's operating costs; and is subject to individual rationality constraints, namely... and .

[0243] The profit maximization is:

[0244] (29)

[0245] in It is the sum of the prices of all buyer query charts within the current transaction period; For penalties, such as fines for breach of SLA.

[0246] In this embodiment, as Figure 5 As shown, the pricing management platform uses backward induction to solve the platform optimization problem by integrating the responses of sellers and buyers. Specifically, it updates the pricing p, profit sharing θ, privacy parameter ε, and view combination Z to maximize the platform's objective function. To ensure the equilibrium is solvable, the platform's objective function is designed as a concave function.

[0247] For any trading period, an alternating optimization strategy based on Stackelberg game theory is used to solve for the platform parameters for the next trading period; specifically including:

[0248] Initialize platform parameters, including: price vector Profit sharing ratio and privacy parameters And obtain the query graph provided by each buyer in the current transaction cycle. candidate view clusters .

[0249] In this embodiment, the platform parameter initialization methods include two types: an initialization method based on the average of historical data (for scenarios with historical data) and an initialization method using preset heuristic rules (for scenarios without historical data).

[0250] Retrieve platform parameters for the current trading period: Price Vector Profit sharing ratio Privacy parameters Combined selection with view .

[0251] For each seller By maximizing the seller's revenue function, the seller's profit can be determined. The optimal response includes: shelf placement decision Supply and quality level .

[0252] For each buyer By maximizing the buyer's utility function, the buyer's value can be determined. The optimal response; the buyer The optimal response is the purchase ratio. .

[0253] In this embodiment, the seller and buyer problems are solved in parallel based on the platform parameters in the current transaction cycle. For each seller i, a convex optimization problem (maximizing the seller's profit function) is solved using CVXPY or the projected gradient method. For each buyer... One-dimensional concave optimization problems (maximizing the buyer's utility function) can be solved using closed-form solutions or bisection methods.

[0254] Collect the optimal responses from all sellers and buyers, denoted as: and .

[0255] from arrive In this embodiment, the outer AO iteration loop is executed. To get 100, the process includes the following steps:

[0256] Fixed profit sharing ratio and privacy parameters The subgradient method is used to maximize the platform objective function, and a price vector constraint is applied. and smoothing regularization constraints To obtain the updated price vector ;in The change in price; To smooth the upper bound of regularization, it is defined by the pricing management platform. ,and . This represents the number of iterations. This represents the maximum number of iterations.

[0257] In candidate view cluster The algorithm employs a greedy approach to maximize the improvement of the platform's objective function, incorporating local swaps or tabu search to address non-convexity and control the query graph. The number of views satisfies Get the updated view combination selection ;in The maximum number of views allowed for each query graph.

[0258] Fixed update price vector Combined selection with view In the interval Internally, the projected gradient method is used to maximize the platform objective function, and L2 regularization constraints are applied. To obtain the updated profit-sharing ratio ;in This represents the change in the profit-sharing ratio; The upper limit of the profit sharing variation range is defined by the pricing management platform.

[0259] Fixed update price vector View combination selection Profit sharing ratio In the interval Within this framework, line search or one-dimensional convex optimization is used to obtain updated privacy parameters. .

[0260] Using the updated price vector View combination selection Profit sharing ratio and privacy parameters Calculate the optimal responses for all sellers and buyers, if the convergence condition is met or Then exit the loop and... , , and Used as a platform parameter for the next trading cycle; otherwise, the cycle continues.

[0261] In this embodiment, convergence is determined as follows: if , It is the convergence threshold, a platform-preset upper limit for the relative change of the objective function, used to determine whether the iteration has converged; The objective function value is the first The platform's revenue function value at the next iteration; It is the first The value of the revenue function after the platform parameters are updated in the next iteration.

[0262] When the pricing management platform detects abnormal behavior, it triggers a fallback mechanism to adjust platform parameters in real time and reassess the response until an equilibrium point is found. The abnormal behavior includes: a low-response mechanism in the current trading cycle that causes sellers not to list items or buyers not to query them; and iterative non-convergence, constraint violations, or a decrease in social welfare during the process of solving for the platform parameters for the next trading cycle. The situation; among which For tolerance threshold, .

[0263] The specific content of the Fallback mechanism is as follows: The following strategies are tried sequentially according to priority:

[0264] F1: Soft Relaxation: Introducing Relaxation Variables And add a penalty to the platform's objective function. .

[0265] F2: Privacy Restricted: .

[0266] F3: Combinatorial Dimensionality Reduction: Shrinking and Prioritize retaining high-quality materials. view.

[0267] F4: Profit Sharing Intervention: ;in For the seller The quality of the subgraph is rated by the platform; This represents the average quality level of all sellers listing sub-images within a given trading period.

[0268] F5: Freeze in batches: Freeze or Optimize first and Query batch processing.

[0269] F6: Simplified Pricing: Temporary Use .

[0270] In each attempt, the outer AO iteration loop is restarted, including the following process:

[0271] Dynamically updated using multi-armed slot machines or UCB algorithms. Based on the seller's performance data (such as quality) recorded by the pricing management platform Retention rate), subject to box constraints.

[0272] Based on the conversion rate, rejection rate, customer satisfaction, and cost-effectiveness indicators statistically analyzed by the pricing management platform, update the integration weights in the basic pricing rules.

[0273] Statistically analyze the fallback trigger frequency and dynamically adjust the regularization strength based on the fallback trigger frequency. , , and slack punishment This embodiment employs a deep learning approach to achieve hyperparameter self-tuning based on the fallback trigger frequency.

[0274] Example 3:

[0275] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the anti-arbitrage pricing method for subgraph data query based on three-party game theory.

[0276] The electronic device may be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the anti-arbitrage pricing method for subgraph data query based on three-party game theory as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0277] The processor is used to execute all or part of the steps in the anti-arbitrage pricing method for subgraph data query based on three-party game theory as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0278] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the anti-arbitrage pricing method for subgraph data query based on three-party game theory described in the above embodiments.

[0279] Example 4:

[0280] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0281] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the anti-arbitrage pricing method for subgraph data query based on three-party game theory described in various embodiments of this application.

[0282] The storage media include: flash memory, hard disk, multimedia card, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disk, optical disk, server, APP application store, and other media that can store program verification codes. These media store computer programs, and when executed by a processor, they can implement the various steps of the anti-arbitrage pricing method based on subgraph data query in a three-way game described above.

[0283] Example 5:

[0284] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned anti-arbitrage pricing method for subgraph data query based on three-party game theory.

[0285] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0286] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0287] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.

Claims

1. An arbitrage-proof pricing system for subgraph data query based on a three-party game, characterized in that, The system comprises three types of participants involved in data transaction: sellers, buyers and a pricing management platform; The seller is configured to upload original sub-graphs owned by the seller to the pricing management platform for data transaction according to a transaction mechanism published by the pricing management platform; The buyer is configured to submit a query graph to the pricing management platform according to the transaction mechanism published by the pricing management platform and the original sub-graphs uploaded by the seller; The buyer is configured to obtain a result graph provided by the pricing management platform according to the query graph and pay a fee for the result graph; The pricing management platform is configured to publish a transaction mechanism for each transaction period; and price the original sub-graphs uploaded by the sellers based on the transaction mechanism. The pricing management platform is configured to integrate the original sub-graphs from one or more sellers to generate a global data graph and build a view set; receive a query graph uploaded by a buyer and query a result graph satisfying the query graph from the view set; and price the result graph based on the transaction mechanism. The pricing management platform is configured to calculate a fee to be paid by the buyer and complete the data transaction according to the calculated fee; and record transaction data for each transaction period and use the transaction data to optimize the transaction mechanism and platform parameters for a next transaction period.

2. The anti-arbitrage pricing method of subgraph data query based on three-party game, implemented by the anti-arbitrage pricing system of subgraph data query based on three-party game of claim 1, characterized in that, The method comprises the following processes: The pricing management platform publishes a transaction mechanism and platform parameters for a current transaction period to all sellers and buyers; Any seller After observing the transaction mechanism, the seller's revenue function is endogenously expected, and based on the revenue maximization principle, the seller Upload the original subgraph of the decision, and declare the data attribute set of the original subgraph; The pricing management platform prices each original sub-graph uploaded by a seller based on the transaction mechanism; The pricing management platform integrates all original sub-graphs uploaded by all sellers by using a graph fusion and consistency checking algorithm to generate a global data graph , and constructs a view set ​ Any buyer After observing the transaction mechanism and the original sub-graph uploaded by all sellers, the buyer's utility function is endogenously expected, and based on the utility maximization principle, the buyer Decides the query graph submitted by the pricing management platform and declares the data attribute set of the query graph; Pricing management platform based on buyer Submitted query graph, from view set The query returns a combination of views that match the query graph as the result graph; at the same time, the corresponding set of sellers is obtained; The pricing management platform prices the result graph based on the transaction mechanism and the buyer pays the fee; and distributes the fee paid by the buyer to all sellers in the seller set based on the pricing of the original sub-graphs by the pricing management platform, thereby completing the data transaction. After completing the data transaction for the current transaction period, the pricing management platform updates the transaction mechanism and platform parameters for a next transaction period based on a dynamic strategy of Stackelberg game. In each transaction period, when the pricing management platform detects abnormal behavior, the pricing management platform adjusts platform parameters in real time by triggering a fallback mechanism. 3.The method of claim 2, wherein, The transaction mechanism comprises a basic pricing rule, an anti-arbitrage constraint and a view combination rule. The specific content of the basic pricing rule is as follows: Any seller... The uploaded original sub-image is used as the sub-image to be priced. And based on the global data graph maintained in the pricing management platform during the current trading cycle. Calculate the subgraph to be priced using the subgraph contribution pricing rule. In the global data graph Shapley values ​​in the graph; using influence pricing rules, calculate the subgraph to be priced. The global data graph The fusion influence score is calculated; the calculated Shapley value and fusion influence score are normalized, and then the normalized Shapley value and fusion influence score are weighted and summed to obtain the subgraph to be priced. Pricing; The specific content of the anti-arbitrage constraint is: for any to-be-priced view , defining the conflict set of the to-be-priced view ; using a weighted set cover function to assign a base price to each sellable base view in the pricing management platform; for any to-be-priced view , finding all base view combinations that can cover the conflict set from all base views, and calculating the price of each base view combination according to the anti-arbitrage pricing function and taking the minimum value as the pricing of the to-be-priced view . The specific content of the view combination rule is: for any query vertex in the query graph , a candidate set of query vertices is constructed ; the candidate set is the set of all vertices in the view set ; the candidate set of query vertices is filtered based on the pseudo-star isomorphism constraint ; all filtered candidate view vertices are added to the queue Queue, and then the queue Queue is recursively pruned based on the ping-pong filtering strategy to obtain the refined candidate set; Based on the refined candidate set, a candidate view containing all candidate view vertices in the refined candidate set is generated, and then a view dependency graph is constructed by calculating the dependency strength between all candidate views. Based on a predefined priority criterion, a priority score of each candidate view in the view dependency graph is calculated, thereby generating an optimal view combination order of the query graph. A view-level bi-graph index is constructed for pre-storing the connection relationship between vertices of each pair of candidate views in the global data graph. According to the optimal view combination order of the query graph, all possible view combinations are recursively enumerated, and in the process of recursive enumeration, the view-level bi-graph index is verified, and then effective view combinations isomorphic to the query graph are retained according to the verification result, and then a result graph of the query graph is generated according to the effective view combinations. The platform parameters include a price vector , a revenue sharing ratio , a privacy parameter , and a view combination selection . 4.The method of claim 3, wherein, The sub-graph contribution pricing rule is: for the global data graph maintained in the pricing management platform in the current transaction period The corresponding view set , randomly sample the view set , obtain sub-samples; respectively calculate the marginal contribution of each sub-sample set to the global data graph ; According to the subgraph to be priced With the node overlap and edge connectivity between each sampling subgraph, assign a structural weight to the marginal contribution of each sampling subgraph to the global data graph ; Based on each sampling subset, the global data graph The marginal contribution and the structural weights assigned to that marginal contribution are used to calculate the subgraph to be priced. In the global data graph Shapley value in; The influence pricing rule is as follows: based on the influence propagation model, using the subgraph to be priced. As seed nodes, Monte Carlo simulation is used. The information propagation process is run once, and calculations are performed. The average number of nodes activated after the end of each information propagation process is used as the subgraph to be priced. The influence of communication; calculating the structural indicators of the to-be-priced subgraph based on a structural indicator model performing a weighted sum on the propagation influence and the structural indicators of the to-be-priced subgraph to obtain a fusion influence score of the to-be-priced subgraph .

5. The method of claim 4, wherein, The arbitrary seller After observing the transaction mechanism, the method of endogenously expecting the seller revenue function is: an arbitrary seller After observing the transaction mechanism, determining the seller The seller decision variable ; The seller decision variable , including: supply quantity , quality level and privacy cost parameter ; and the seller decision variable Satisfy the predefined capacity constraints, quality level constraints, quality constraints and historical reputation score constraints; Based on the transaction mechanism, the seller's decision variable is defined as The seller's payoff function, denoted as is defined as ； wherein represents the revenue of the seller; represents an indicator function; is the pricing for the query graph ; represents the share of the seller ; is the cost function of the seller , , , and are cost coefficients of the seller .​ a set of data attributes of the original subgraph, including: quality level freshness and privacy cost parameters .

6. The method of claim 5, wherein, the arbitrary buyer After observing the trading mechanism and the original subgraphs uploaded by all sellers, the method of endogenously anticipating the buyer utility function is that the arbitrary buyer After observing the trading mechanism and the original subgraphs uploaded by all sellers, the method of determining the buyer The buyer decision variable of the buyer , including: purchase ratio , single query budget allocation , multi-query total budget and privacy tolerance ; and the buyer decision variable satisfies the predefined constraint conditions, including: total budget constraint, privacy compliance constraint, single query price constraint and multi-query budget constraint; Based on the transaction mechanism, the buyer's decision variable is defined as: The buyer's utility function is defined as: The buyer's utility function is defined as: The buyer's utility function is defined as: ； wherein represents the utility of the buyer ; represents the subjective utility weight of the buyer j is the coverage benefit is the privacy benefit is the quality assessment a data attribute set of the query graph, comprising: a purchase proportion , an SLA level , and a privacy tolerance .

7. The method of claim 6, wherein, The method for pricing the result graph by the pricing management platform according to the transaction mechanism is as follows: Based on the result graph GFT pricing rules, for the result graph containing Each of the small views defines a view signal; constructing a result map a graph laplacian and performing spectral decomposition to obtain a result map a matrix of eigenvectors a feature vector matrix of the result image, the feature vector matrix comprising a plurality of feature vectors, each feature vector comprising a plurality of feature vector elements, each feature vector element being associated with a respective one of the plurality of pixels of the result image, and each feature vector element being indicative of a respective one of the plurality of pixel values of the respective one of the plurality of pixels of the result image, a GFT coefficient of the respective one of the plurality According to the graph Fourier transform, GFT, coefficients of each small view, compute a spectral domain contribution degree for each small view to the result image spectrum domain According to the spectral domain contribution degree of each small view, the base prices of all small views are weighted and summed to obtain a result image The base pricing For the result image Perform sensitivity analysis and evaluate the results based on the preset indicators. To mitigate privacy risks, differential privacy theory is employed to set a privacy protection budget for the pricing management platform based on the risk assessment results. ; determine whether to trigger a perturbation based on a predefined multi-trigger condition, and if the perturbation is triggered, determine whether to trigger a perturbation based on a privacy protection budget select a differential privacy noise mechanism, and re-utilize the selected differential privacy noise mechanism on the result map inject noise, and update the result map if the perturbation is not triggered, retain the original result map ; The current result graph is evaluated using multiple predefined quality indicators. Perform a data quality assessment and generate the current result graph based on the assessment results. Quality adjustment factor; based on a predefined privacy discount function, according to a privacy protection budget computing a current result map of a privacy protection strength; the current result map a quality adjustment coefficient, a privacy protection strength, and a product of a base pricing of the result map as the pricing of the result map the current result map 8.The method of claim 7, wherein, The specific content of whether to trigger disturbance based on the predefined multi-trigger condition is as follows: evaluating the result map according to predefined multi-trigger conditions and obtaining evaluation results of each trigger condition respectively; The predefined multiple triggering conditions include: structural uniqueness check: result diagram The node's k-hop neighborhood signature uniqueness score exceeds 0.7; Node degree anomaly check: Result diagram Moderate degree or above The proportion of nodes exceeds 0.6; among them Standard deviation of degree for all nodes; Sensitive attribute check: Result plot Nodes with sensitive attributes exist; overlap check: result image The overlap with the query graph exceeds 80%; Based on the GraphPerturbationDecider class, a weighted sum of all evaluation results of the result graph is performed to obtain a risk score of the result graph , and the perturbation is triggered when the risk score > 0.5 or the privacy protection budget <1.

0. 9.The method of claim 8, wherein, Platform decision variables of the pricing management platform , including: price vector , distribution ratio , privacy parameter , view combination selection , and distribution share ; According to the platform decision variable Defining a platform objective function of the pricing management platform, including: maximizing social welfare or maximizing profit; The social welfare maximization is as follows: ； wherein represents the buyer utility; represents the seller revenue; and has and ; represents the platform operating cost; The profit maximization is as follows: ； wherein is the sum of the prices of all buyer queries graph in the current transaction cycle; is the penalty term; For any transaction cycle, the platform parameters of the next transaction cycle are solved by using an alternating optimization strategy based on Stackelberg game. 10.The method of claim 9, wherein, The specific content of the platform parameters of the next transaction cycle are solved by using an alternating optimization strategy based on Stackelberg game. Initializing platform parameters, including: price vector , revenue sharing ratio and privacy parameter ; and obtaining candidate view clusters of query graph provided by each buyer in the current transaction period Obtaining platform parameters in the current transaction period: price vector , distribution ratio , privacy parameter and view combination selection ; For each seller , the optimal response of the seller , including: listing decision , supply quantity and quality level , is determined by solving the seller's revenue function maximization For each buyer , the optimal response of the buyer is determined by solving the maximization of the buyer's utility function; the optimal response of the buyer is the purchase proportion ; Collecting the optimal responses from all sellers and buyers, from to Performing outer AO iteration loop, including the following processes: fixing the revenue sharing ratio and privacy parameter , maximizing the platform objective function using subgradient method, and imposing price vector constraints and smoothness regularization constraints to obtain the updated price vector ; wherein is the iteration number; is the maximum iteration number; At candidate view cluster The greedy algorithm is executed on the updated view combination selection ; Fixed updated price vector And view combination selection In the preset interval, the projection gradient method is used to maximize a platform objective function, and an L2 regularization constraint is applied to obtain an updated distribution ratio ; Fixed updated price vector , view combination selection and revenue sharing ratio , in the preset interval, the line search or one-dimensional convex optimization is used to solve, and the updated privacy parameter is obtained ; Utilizing updated price vector , view combination selection , revenue sharing ratio , and privacy parameter Compute the optimal response of all sellers and buyers, if the convergence condition is met or , exit the loop and set , , , and as the platform parameters for the next trading period; otherwise, continue the loop.

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