A differential privacy trajectory publishing method, system, device and medium

Abstract

The application discloses a differential privacy trajectory publishing method, system, device and medium, relates to the technical field of trajectory publishing, and comprises the following steps: acquiring original user trajectory data satisfying differential privacy; identifying a key parameter set affecting the original user trajectory data; performing joint optimization on the key parameter set through an improved flow direction algorithm, taking minimizing a predefined fitness function as an objective, and obtaining an optimal parameter combination; the improved flow direction algorithm is based on an original flow direction algorithm, introduces chaotic mapping initialization for key parameter set initialization, introduces an adaptive neighborhood generation mechanism for dynamically adjusting the neighborhood quantity of the fitness of water flow individuals, and performs parallel fitness calculation for fitness acquisition; performing noise adding and pruning operations on the original user trajectory data by using the optimal parameter combination, generating and publishing final user trajectory data. Through the improved algorithm, the application automatically adjusts the parameters of the personalized noise prefix tree trajectory publishing, and promotes the progress of the differential privacy trajectory publishing.

Description

Technical Field

[0001] This invention relates to the field of trajectory publishing technology, and in particular to a differential privacy trajectory publishing method, system, device and medium. Background Technology

[0002] With the rapid rise of mobile computing and the Internet of Things (IoT), location-based services (LBS) have become integrated into daily life, generating massive amounts of trajectory data. This data provides valuable insights for urban planning, traffic management, and personalized recommendations. However, because trajectories record fine-grained spatiotemporal behavior, their unauthorized publication can expose sensitive locations (such as homes or workplaces), thus threatening personal privacy. Therefore, achieving high analytical utility while ensuring strict privacy is a key challenge. DP (Proof-of-Service) provides provable protection independent of attackers' prior knowledge and is considered the gold standard for trajectory data publication.

[0003] Within the differential privacy paradigm, numerous deployment schemes have been proposed, with prefix tree-based methods standing out particularly due to their ability to capture sequence statistics and support efficient querying. By leveraging shared prefixes, prefix trees hierarchically store counts and support prefix and frequent sequence queries, thus advancing tasks such as pattern mining and path prediction. Their hierarchical structure also facilitates noise calibration and flexible budget allocation, while pruning can further enhance utility.

[0004] However, when publishing privacy-preserving trajectories, the prefix tree-based mechanism relies on several interrelated parameters: spatial encoding granularity (e.g., Hilbert curve or GeoHash), hierarchical budget allocation, and pruning threshold. These parameters collectively determine the trade-off between privacy and utility. Existing research employs simplified assumptions (such as uniform budget allocation) and grid search to handle the associated parameters during privacy-preserving trajectory publishing. While these methods can optimize a small number of parameters, they exhibit significant variability across different datasets and scenarios. Furthermore, as the dimensionality of parameters increases and evaluation costs rise, computational resource constraints make it difficult to cover the globally optimal region. Consequently, existing methods struggle to maintain the availability of trajectory data while ensuring user privacy in user trajectory publishing scenarios such as location services, traffic flow analysis, and personalized urban planning. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a differential privacy trajectory publishing method, system, device, and medium to solve the problems in the prior art.

[0006] The present invention specifically provides the following technical solution: A method for publishing differential privacy trajectories includes the following steps: Obtain raw user trajectory data that satisfies differential privacy; Identify the set of key parameters that affect the original user trajectory data; the set of key parameters includes: Hilbert curve order, total privacy budget, prefix tree hierarchical privacy budget allocation strategy, and pruning threshold. The improved flow direction algorithm performs joint optimization of the key parameter set to minimize the predefined fitness function and obtain the optimal parameter combination. The improved flow direction algorithm is based on the original flow direction algorithm, introduces chaotic mapping initialization for initializing the key parameter set, introduces an adaptive neighborhood generation mechanism to dynamically adjust the number of neighborhoods for the fitness of individual water flow, and obtains fitness through parallel fitness calculation based on Spark. The original user trajectory data is subjected to noise addition and pruning operations with the optimal parameter combination to generate and publish the final user trajectory data.

[0007] Preferably, the step of jointly optimizing the key parameter set using an improved flow direction algorithm to minimize a predefined fitness function and obtain the optimal parameter combination specifically involves: Determine the initial set of key parameters; The initial key parameter set is processed using chaotic mapping to generate an initial solution; wherein, each set of parameters in the initial key parameter set corresponds to an initial solution in the flow direction algorithm, i.e., a water flow; With the goal of minimizing the predefined fitness function, the fitness of the water flow is evaluated for each initial solution based on the parallel fitness computation of Spark. The evaluated fitness is used to generate an adaptive neighborhood, and the fitness of the water flow is evaluated again after the adaptive neighborhood is generated to select the best neighborhood. When the fitness of the best neighborhood is less than the fitness of the current flow, a random number is generated, and the current flow is directed to the random number of best flows. The fitness of the flows is evaluated again, the best flow is selected, and the updated flow position is used as the optimal parameter combination.

[0008] Preferably, the objective of minimizing the predefined fitness function specifically includes: The fitness function is obtained by weighting the mean relative error (ARE), the Kullback-Leibler divergence (KLD), and the normalization penalty term adjusted for the order of the Hilbert curve. The specific expression is as follows: ; To obtain the minimum predefined fitness function, the specific expression is: ; in, For the fitness function, This is a normalization penalty term for adjusting the order of the Hilbert curve. The order of the Hilbert curve Adjustments It is the total privacy budget. It is a privacy budget allocation strategy at the prefix tree level. It is the pruning threshold. This represents the threshold parameter.

[0009] Preferably, the adaptive neighborhood generation based on the evaluated fitness specifically involves: The number of generated neighborhoods is dynamically adjusted based on the evaluated fitness; fitness is positively correlated with the number of generated neighborhoods, as shown in the following expression: ; in, MaxSize It is the maximum value of the number of neighbors. It is a constant. It is the number of neighborhoods. It represents the fitness of the worst-fitting individual in the current water flow population. It refers to the size of the water flow population. It is the first The adaptability of the water flow It is the first The location of the water flow.

[0010] Preferably, the Spark-based parallel fitness computation evaluates the fitness of the water flow for each initial solution, specifically as follows: Transform the initial solution to be evaluated into a Spark Resilient Distributed Dataset RDD; Based on Spark Resilient Distributed Dataset (RDD), the fitness of each initial solution is obtained in parallel, and the obtained fitness results are summarized to obtain the fitness of all water flows.

[0011] Preferably, the acquisition of raw user trajectory data that satisfies differential privacy specifically includes: The collected raw user trajectory data is grouped under spatiotemporal constraints to construct several trajectory equivalence classes; For the spatial distribution of points within each trajectory equivalence class, the optimal Hilbert order is selected, and representative points are selected from the trajectory equivalence class. The Hilbert curve is traversed under the optimal Hilbert order, and the geographical coordinates of the traversed representative points are converted into one-dimensional strings using the staggered position rule. A one-dimensional string is inserted into the prefix tree, noise is added to the count values ​​stored in the prefix tree, and a preset privacy budget is allocated to the prefix tree; the prefix tree after the privacy budget allocation is pruned based on a preset pruning threshold to generate original user trajectory data that satisfies differential privacy.

[0012] Preferably, when performing spatiotemporal constraint grouping on the collected raw user trajectory data, the raw user trajectory data whose start and end timestamp deviations are both within the threshold are grouped into different trajectory equivalence classes.

[0013] This invention provides a differential privacy trajectory publishing system, comprising: The data acquisition module is used to acquire raw user trajectory data that satisfies differential privacy. The identification module is used to identify a set of key parameters that affect the original user trajectory data; the set of key parameters includes: Hilbert curve order, total privacy budget, prefix tree hierarchical privacy budget allocation strategy, and pruning threshold. The optimization module is used to jointly optimize the set of key parameters through an improved flow direction algorithm, with the goal of minimizing the predefined fitness function to obtain the optimal parameter combination. The improved flow direction algorithm is based on the original flow direction algorithm, introduces chaotic mapping initialization for initializing the set of key parameters, introduces an adaptive neighborhood generation mechanism to dynamically adjust the number of neighborhoods for the fitness of individual water flow, and obtains fitness through parallel fitness calculation based on Spark. The final publishing module is used to perform noise addition and pruning operations on the original user trajectory data with the optimal parameter combination to generate and publish the final user trajectory data.

[0014] The present invention provides a computer device, including a memory and a processor. The memory stores a program, and when the program is executed by the processor, the processor performs the steps of the above-described differential privacy trajectory publishing method.

[0015] The present invention provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the differential privacy trajectory publishing method described above.

[0016] Compared with the prior art, the present invention has the following significant advantages: This invention proposes a trajectory publishing method based on a parallel improved flow direction algorithm, using a set of key identified parameters. The method optimizes the overall flow direction by minimizing the fitness function. It introduces chaotic mapping initialization into the original flow direction algorithm, utilizing the ergodicity and uniformity of the chaotic sequence to generate an initial solution. An adaptive neighborhood generation mechanism dynamically adjusts the number of neighborhoods based on the fitness of individual flow streams in the initial solution. Parallel fitness calculation is implemented using the Spark framework, transforming the parameter set to be evaluated into a resilient distributed dataset for distributed processing. This significantly reduces the time overhead of large-scale parameter optimization. The method enables the trajectory publishing scheme to adaptively configure the Hilbert curve order, privacy budget allocation strategy, and pruning threshold based on user trajectory data, adapting to different real-world scenarios such as urban planning, traffic management, and personalized location recommendations. While meeting strict privacy compliance requirements, it ensures the usability of trajectory data in critical tasks such as frequent path mining and hotspot area identification, effectively supporting the coordinated optimization of privacy protection and data utility in real-world scenarios. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the D8 method in this invention; Figure 2 This is a flowchart illustrating the overall workflow of this invention. Figure 3 This is a diagram showing the distribution of chaotic mappings in this invention; Figure 4 This is a flowchart of SP-IFDA in this invention; Figure 5 This is the optimal fitness curve in this invention; wherein, Figure 5 (a) is the optimal fitness curve for BJ-Day3. Figure 5 (b) is the optimal fitness curve for BJ-Day7; Figure 6 This is a diagram illustrating the scalability experiment on BJ-Day3 in this invention; wherein, Figure 6 (a) is the time consumption graph. Figure 6 (b) is the speedup ratio diagram; Figure 7 This is a comparison result diagram of ARE in this invention; wherein, Figure 7 (a) is a comparison of ARE results for 'hbs' in BJ-Day3. Figure 7 (b) is a comparison of the ARE results when 'hbs@' is in BJ-Day3; Figure 7 (c) is a comparison of ARE results for hbs'in BJ-Day7. Figure 7 (d) is a comparison of ARE results when 'hbs@' is in BJ-Day7; Figure 8 This is a flowchart of a differential privacy trajectory publishing method provided by the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0019] Trajectory data, a digital record of an individual's spatiotemporal activities, underpins applications in various fields such as urban computing, intelligent transportation, and public health. Because this data reflects users' movement patterns and activity ranges, it may reveal sensitive locations (such as homes or workplaces), thus uncontrolled sharing poses a significant risk of privacy breaches. Traditional anonymization techniques, such as k-anonymity and its variants, attempt to mitigate these risks through generalization or suppression. However, numerous studies have shown that these techniques offer limited protection against attackers with background knowledge or linking attacks and lack stringent, quantifiable privacy guarantees.

[0020] Discrete trajectories (DP) provide a provable privacy framework unaffected by attackers' prior knowledge and have become the de facto standard for trajectory data publication. Researchers have developed various DP-based methods leveraging the unique characteristics of trajectory datasets. The first major branch focused on publishing aggregated statistics or synthesizing new datasets. A typical approach is to divide the geospatial area into a grid and apply Laplace noise to the counts of trajectory points or segments within each cell, thereby generating privacy-preserving heatmaps or flow maps. Recent work has generated differentially privacy-preserving synthetic trajectories that retain key statistical properties such as spatial distribution and transition probabilities while preventing individual disclosure.

[0021] The second important branch uses specialized data structures to organize trajectories and enforces differential privacy at the structural level to support sequence pattern queries. Tries efficiently capture sequence features and support frequent pattern mining, path prediction, and prefix counting. In these frameworks, trajectories are first encoded using methods such as Hilbert-GeoHash and then inserted into a trie, whose nodes store statistics perturbed by Laplace noise to satisfy differential privacy. Alternative structures, such as quadtrees, are also employed to preserve spatial proximity.

[0022] Recent research has further enhanced utility under differential privacy constraints. By combining temporal hierarchies with mixed parameter spaces and clustering-based generalization, index structure and noise allocation in DPTD are optimized to achieve efficient range counting queries. Differential privacy is also combined with Markov models in the adaptive order framework PrivTrace. Despite these advances, a fundamental challenge remains: how to maximize data utility under a fixed privacy budget.

[0023] Evolutionary Algorithms and Optimization Problems in Trajectory Data Privacy Preservation: In the field of trajectory data privacy preservation, dynamic programming (DP) has become the gold standard for privacy protection, but its practicality is highly dependent on parameter configuration. Therefore, many studies have explored heuristic optimization methods, especially evolutionary algorithms, to automate parameter tuning. This paper combines NoisyMin, improved gradient clipping, and descent methods to optimize the noise scale and learning rate in training DP deep models. An algorithm is also proposed to optimize the budget allocation for non-interactive smart card trajectory publishing. However, these methods typically rely on scenario-specific heuristics or manual tuning, lacking a general global optimum search mechanism.

[0024] A significant milestone was the GAPBAS algorithm, which explicitly employs a genetic algorithm to optimize budget allocation in DP k-means clustering and demonstrated a significant utility improvement in experiments. However, GAPBAS, for clustering tasks and global budget proportions, fails to fully utilize the inherent properties of hierarchical structures (such as prefix trees) and does not jointly optimize all key parameters that determine the overall framework performance. Furthermore, its optimization objective is limited to budget proportions, neglecting crucial factors such as spatial encoding granularity and pruning strategies, which are essential for high-quality trajectory delivery.

[0025] Specifically, nodes at different depths in a prefix tree exhibit diverse characteristics—such as query importance and noise accumulation—therefore, effective budget allocation must adhere to depth-dependent constraints or functional forms. For example, the baseline work of this invention employs a logarithmic growth model with adjustable parameters to control the budget growth rate. This method also includes selecting the Hilbert curve order and setting a depth-based pruning threshold, which collectively shape the privacy-utility tradeoff. GAPBAS's general scaling strategy fails to incorporate such prior knowledge or constraints. Furthermore, its optimization objective is limited to budget scaling, neglecting crucial factors such as pruning strategies and spatial encoding granularity—elements indispensable for high-quality trajectory publishing.

[0026] Evolutionary algorithms are optimization algorithms that start from an initial solution and iterate until a termination condition is met. Researchers have developed various population evolutionary algorithms by simulating the collective behavior of biological groups in nature. Population evolutionary algorithms inspired by biological group behavior include Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), Squirrel Search Algorithm (SSA), and Arithmetic Optimization Algorithm (AOA). Recently, a novel physics-based evolutionary algorithm called FDA has been proposed. This algorithm simulates the direction of water flow in a watershed towards the lowest elevation outlet point, demonstrating a unique mechanism in solving various global optimization problems. Despite its simple structure, FDA shows considerable potential in solving engineering challenges. However, existing research indicates that FDA often encounters difficulties in escaping local optima, limiting its ability to explore a wider search space.

[0027] Knowledge related to trajectory data: Definition 1: Spatiotemporal trajectory sequence. Within a given spatiotemporal domain, the historical path of a moving object is represented by an ordered sequence of sampled positions. Formally, the trajectory T is defined as:

[0028] (1); in Represents the i-th sampling point ( ), In timestamp The observed geographic coordinates and timestamps satisfy The integer n is the total number of sampling points in the trajectory T.

[0029] Definition 2: Trajectory Dataset. Let... It is the collection of all sampling points gathered within the study area and time window. A set of independent trajectories constitutes the trajectory dataset D:

[0030] (2); Where m is the number of trajectories contained in the dataset.

[0031] Definition 3: Trajectory Equivalence Classes. Given a trajectory dataset D and a time tolerance... If a reference start time exists and reference end time This makes each trajectory equivalence class satisfy:

[0032] (3); Then it is called This is the trajectory equivalence class. Parameters Granularity for controlling temporal similarity.

[0033] Knowledge related to differential privacy: Definition 4: - Differential privacy. Randomized algorithm. satisfy - Differential privacy, if for any adjacent datasets D and D' (difference of at most one record) and any measurable subset ,have:

[0034] (4); Where the nonnegative parameter Privacy budget: smaller It offers stronger privacy protection, but at the cost of reduced data utility.

[0035] Definition 5: Differential privacy mechanism and combinatorial theorem: (1) Laplace mechanism: for numerical queries Add independent and identically distributed noise, and sample from ,in It refers to global sensitivity.

[0036] (2) Exponential mechanism: Given a candidate set R and a utility function Its sensitivity is With probability and Output in a proportional manner .

[0037] Execute in sequence with privacy budget The mechanism, the overall budget is The mechanism is executed on disjoint subsets of the dataset, and the overall budget is... .

[0038] Other relevant information about trajectory data publishing: Definition 6: Hilbert-Geohash Encoding. Hilbert-Geohash maps two-dimensional coordinates (e.g., longitude and latitude) to one-dimensional strings. Similar to Geohash, it uses a hierarchical grid, but traverses the cells by filling curves in Hilbert space to enhance spatial locality. The string length corresponds to the spatial resolution.

[0039] Definition 7: Trie. A trie is an ordered tree used for efficiently storing and retrieving a set of strings or sequences. Each edge represents a symbol; a path from the root to any node corresponds to a unique prefix. By sharing common prefixes, tries achieve compact storage and fast prefix lookup.

[0040] Definition 8: Threat Model. This invention assumes an adversary observes a published privacy-preserving dataset D' and possesses arbitrary auxiliary knowledge. The adversary's goal is to infer sensitive user information by associating D' with contextual data.

[0041] Definition 9: c-Geographical indistinguishability. A random mechanism K maps the real location x to the reported location z. If for any x, x', and z,

[0042] (5); in If K is the Euclidean distance, then K satisfies c-geographical indistinguishability, ensuring that reports generated from neighboring locations are statistically similar.

[0043] FDA (Physics-Based Optimization) is a novel physics-based optimization algorithm that has gained widespread attention across multiple fields for solving optimization challenges. It conceptualizes the problem as a black box, facilitating its application to a broad range of optimization scenarios. FDA draws inspiration from methods for evaluating direct runoff in watersheds. In a watershed, direct runoff is defined as the amount of water retained on the surface after precipitation (after deducting losses such as interception, evaporation, transpiration, and infiltration). Jenson et al. developed the D8 method, a widely accepted approach for determining runoff direction. This method assumes that water can flow to one of eight adjacent cells. Each cell is considered to have eight adjacent cells, each with specific elevation and distance metrics relative to the center cell. By comparing the elevation and distance differences between the center cell and its adjacent cells, the slope of each cell is determined, and the water flow in each cell is directed to the adjacent cell with the steepest slope. Figure 1 A schematic diagram of the D8 method is shown.

[0044] When examining a watershed, the D8 method is first used to determine the direction of water flow throughout the area. Then, each cell is assigned a value corresponding to the number of cells that flow towards that cell. The cell with the highest value is then identified as the watershed's outlet point. Additionally, cells with lower elevations relative to their adjacent cells are identified as depressions and should be appropriately filled. The FDA aims to determine the direction of water flow within the watershed and subsequently convert rainfall into runoff. The FDA bases its assessment on the following assumptions:

[0045] (1) Each stream has a location and a height. (2) Each stream is surrounded by... Each water flow has a height or objective function. (3) The water flow velocity is proportional to the slope. (4) The water flow direction is the direction with the lowest slope. (5) The outlet point of the watershed is the water flow location with the optimal objective function.

[0046] The following is an overview of the FDA's core steps: Initialize the flow location: FDA's initial parameters include the flow population size. Number of neighboring areas The initial position of the water flow is determined by the following formula: neighborhood radius c and maximum iteration count MaxIter.

[0047] (6); in, Indicates the position of the i-th water flow; and These are the upper and lower limits of the decision variable, respectively; It is a random number, and , which follows a uniform distribution.

[0048] Generation of neighborhood: The FDA assumes that each water flow has a neighborhood around it. Each neighborhood is represented by a given number of units. Its position is generated using the following formula:

[0049] (7); in, Indicates the position of the i-th neighborhood; It is a random number that follows a normal distribution with a mean of 0 and a standard deviation of 1. The FDA uses the following formula to linearly reduce... This achieves a balance between global and local search capabilities:

[0050] (8); in, It is a random number that follows a uniform distribution; The random position is generated by formula (6); It is a non-linear weight whose value varies randomly between 0 and infinity. As the number of iterations increases, It will get closer and closer Ultimately, the Euclidean distance between the two becomes 0. The local search is then complete. The calculation is as follows:

[0051] (9); Iter represents the current iteration round. and Represents random numbers and random vectors that follow a normal distribution.

[0052] Update water flow location: The water flow moves at a velocity V towards the neighborhood with the optimal target value, and its velocity is proportional to the slope. The formula for calculating V is as follows:

[0053] (10); in, It is a random number that follows a uniform distribution; S represents the slope vector from the neighborhood to the current water flow position. The slope of water flow i relative to neighborhood j. It is determined by the following formula.

[0054] (11); in, d represents the fitness of the objective function; d represents the dimension of the problem.

[0055] New water flow location The calculation formula is as follows: (12); It is important to emphasize that the objective function of any neighborhood involved in this process cannot be lower than the objective function of the water flow. This principle can be analogized to the process of filling a tank, which determines the direction of the water flow. To simulate the above state, the FDA uses a method of randomly selecting alternative water flows, as shown in the following equation:

[0056] (13); Where r is a random integer; It is a random vector between 0 and 1 that follows a uniform distribution; It is a random number that follows a uniform distribution. Finally, the fitness of the newly generated flow is calculated and compared with the fitness of the previous flow to determine the position of the flow at Iter+1 iterations.

[0057] like Figure 8 As shown, this embodiment provides a differential privacy trajectory publishing method, including the following steps: Step 1: Obtain raw user trajectory data that satisfies differential privacy.

[0058] Figure 2 The overall workflow of this method is described. In short, it first implements a personalized trajectory data publishing scheme based on a noise prefix tree. Then, it identifies parameters that significantly affect the scheme's performance and uses the IFDA algorithm to optimize these parameters, thereby improving the overall utility of the framework. This embodiment presents a differential privacy trajectory publishing method, which includes three tightly coupled stages: trajectory preprocessing, adaptive Hilbert-Geohash (AHGH) encoding and representative point selection, and noise prefix tree construction and DP publishing.

[0059] Step 1.1: Trajectory Preprocessing: A raw user trajectory dataset D is collected and preprocessed to detect and remove invalid samples or points with obviously unreasonable geographic coordinates. Then, the collected raw user trajectory data is grouped under spatiotemporal constraints to construct several trajectory equivalence classes—that is, raw user trajectory data whose start and end timestamp deviations are all within a threshold (Definition 3) are grouped into different trajectory equivalence classes EC. This step supports class-specific privacy budgets and facilitates subsequent personalized processing.

[0060] Step 1.2: Adaptive Hilbert-Geohash (AHGH) Encoding and Representative Point Selection: For each trajectory equivalence class, the optimal Hilbert order is adaptively selected based on the spatial distribution of points within the class, and representative points are selected from the equivalence classes based on an exponential mechanism. For each representative point, the Hilbert curve is traversed at the optimal Hilbert order, and the geographic coordinates of the traversed representative points are converted into one-dimensional strings using Geohash's staggered position rule. Specifically:

[0061] This stage achieves efficient trajectory space representation and compression by combining the locality preservation property of Hilbert space-filling curves and the hierarchical encoding idea of ​​Geohash. First, for each EC, the algorithm adaptively selects the optimal Hilbert order based on the spatial distribution of its points. Based on the characteristics of the Hilbert curve, the order is selected to partition each EC. The order is one of the main parameters optimized in this study. Then, to reduce redundancy and the amount of data that needs to be published, a set of highly representative points is selected based on an exponential mechanism (Definition 5).

[0062] The selected points are converted into one-dimensional strings by traversing the Hilbert curve at a selected order and applying Geohash's staggered bit rule. The string length is adaptively adjusted according to EC sensitivity. These encoded strings, after optional Base64 conversion, form a set D that is passed to the next stage.

[0063] Step 1.3: Noise Prefix Tree Construction and DP Deployment: A one-dimensional string is inserted into a prefix tree, noise is added to the count values ​​stored in the prefix tree, and a preset privacy budget is allocated to the prefix tree. Based on a preset pruning threshold, the prefix tree with the allocated privacy budget is pruned to generate trajectory data that satisfies differential privacy. Specifically:

[0064] The final stage stores the encoded trajectory data in a noisy prefix tree and publishes privacy-preserving statistics. First, the encoded trajectory data is stored in a noisy prefix tree. DEach AHGH string is inserted into the prefix tree; each node stores the number of times the current position point has been traversed as a count value. Then, noise is added to the count values ​​stored in the prefix tree, and a privacy budget is allocated according to a logarithmic growth model.

[0065] (14); Where h is the height of the tree; this formula can allocate more budget to deeper nodes. Finding a better allocation strategy is also one of the main optimization objectives of this invention.

[0066] For each non-leaf node To the true count Add Laplace noise ,in This refers to global sensitivity; to reduce the impact of noise at different levels in the prefix tree, the baseline introduces a level-related threshold. Pruning; if nodes The noise count is lower than If the node and its subtree are not found, then the node and its subtree may be discarded; parameter k and Controlling the aggressiveness of pruning is therefore a key optimization objective.

[0067] The cleaned prefix tree obtained after noise injection and pruning D’ Released for downstream use -DP compatible analysis query; see Algorithm 1 for details.

[0068] Algorithm 1 - Trajectory Data Publishing Method: enter: D , , , Output: Privacy protected The specific processing steps are as follows:

[0069] Preprocessing D get D pro Based on start-end timestamps from D pro Divide the trajectory equivalence classes EC i .

[0070] Foreach do: according to C . HilbertOrderPolicy Adaptive selection HilbertOrder ;choose EC Representative center point CenterPoints use CenterPoints and HilbertOrder Will EC Encoded as EC encode ; .

[0071] End for: from Constructing a prefix tree PT Allocate privacy budget: .

[0072] Add Laplace noise: .

[0073] according to h , k and b Calculate the pruning threshold ; Prune the tree and get .

[0074] Step 2: Identify the set of key parameters that affect the original user trajectory data; the set of key parameters includes: Hilbert curve order, total privacy budget, privacy budget allocation strategy at the prefix tree level, and pruning threshold.

[0075] Optimization Objective: Based on in-depth analysis using baseline methods, four key parameters were identified that significantly impact framework performance and are therefore worthy of system optimization. (1) Hilbert curve order: The order sets the spatial resolution of the AHGH code. Lower orders create coarser cells, shorter code, and shallower trees, but may miss fine-grained spatial patterns. Higher orders improve resolution and locality, but at the cost of longer code, deeper trees, and more accumulated noise. The goal of this invention is to identify an optimal order that achieves the best balance between spatial expressiveness and noise robustness for a given application.

[0076] (2) Total privacy budget As a key DP parameter, The randomness that determines the noise magnitude and the exponential mechanism: smaller This implies stronger privacy and lower utility. While policies are generally fixed, this invention analyzes the framework within a practical range (from strict to lenient privacy) and addresses each... Optimize the remaining parameters (assignment, k, b) to maximize utility.

[0077] (3) Prefix tree level privacy budget allocation strategy: The strategy allocates the total budget to the tree level. The baseline uses logarithmic growth; this allocation method determines that the amount of noise added at different depths will also differ. More budget is allocated to shallower layers to benefit coarse queries, while deeper layers focus on fine-grained queries. This invention compares uniform, arithmetic, logarithmic, and custom schemes to find the allocation that provides the best overall utility or accuracy for a specific query.

[0078] Within the optimization framework, a privacy budget allocation strategy at the prefix tree level. It is another key decision variable. Based on previous research, four strategies were considered, as summarized in Equation (17):

[0079] (17); for ,Will Distribute evenly to each level of the tree; for An arithmetic progression growth strategy will be adopted. First, a small base budget is allocated to the root node, and the remaining levels receive a budget that grows arithmetically; for A logarithmic growth strategy is employed, which scales the budget proportionally to the logarithm of the hierarchy, thus achieving non-linear growth; for A frequency-aware allocation strategy is applied to allocate budgets based on the access frequency or importance of nodes, ensuring that nodes with higher query frequency or importance receive more privacy budget. Hierarchies with higher query frequency or greater importance receive a larger proportion of the privacy budget, thereby maximizing the utility of critical information.

[0080] (4) Pruning thresholds (k, b): Level thresholds The decision to prune nodes affects the size and sparsity of the tree. Higher thresholds result in aggressive pruning—reducing noise but risking the loss of rare patterns, while lower thresholds retain more nodes and noise. This invention adjusts (k, b) to... -DP minimizes query error, aiming to achieve the best trade-off between suppressing noise and not discarding valuable information.

[0081] Step 3: The key parameter set is jointly optimized by the improved flow direction algorithm to minimize the predefined fitness function and obtain the optimal parameter combination. The improved flow direction algorithm is based on the original flow direction algorithm, introduces chaotic mapping initialization to initialize the key parameter set, introduces an adaptive neighborhood generation mechanism to dynamically adjust the number of neighborhoods for the fitness of individual water flow, and obtains fitness through parallel fitness calculation based on Spark.

[0082] This invention optimizes parameters based on SP-IFDA. SP-IFDA differs from the original FDA in four aspects: optimization objective, initialization, adaptive neighborhood size, and parallelization. These are detailed below:

[0083] The optimization objective is to discover the optimal combination of the aforementioned key parameters, thereby significantly improving the privacy-utility trade-off of the baseline framework implementation. To this end, this invention introduces an enhanced heuristic optimization algorithm, SP-IFDA, which systematically adjusts parameters affecting overall performance, such as... Figure 4 As shown. Specifically:

[0084] Step 3.1: Determine the initial set of key parameters.

[0085] Step 3.2: Process the initial key parameter set using chaotic mapping to generate an initial solution; where each set of parameters in the initial key parameter set corresponds to an initial solution in the flow direction algorithm, i.e., a water flow.

[0086] Initial Solution Generation: In traditional heuristic algorithms, randomly generating initial solutions is a crucial step. However, while simple, random number generation methods can lead to insufficient solution diversity. To improve this, this invention employs chaotic mapping to generate initial solutions. Chaotic mapping can generate more uniformly distributed initial solutions, thereby increasing solution diversity. This invention uses two types of chaotic mapping: Logistic Chaotic Map (LCM) and Piecewise Chaotic Map (PCM). The definition of Logistic Chaotic Map is as follows:

[0087] (18); The definition of a piecewise chaotic mapping is as follows: (19); in, The distribution of these two chaotic mappings is as follows: Figure 3 As shown.

[0088] Step 3.3: With the goal of minimizing the predefined fitness function, the fitness of the water flow is evaluated for each initial solution based on Spark's parallel fitness computation. The evaluated fitness is used to generate an adaptive neighborhood, and the fitness of the water flow is evaluated again after the adaptive neighborhood is generated to select the best neighborhood.

[0089] 1. The core of SP-IFDA is a fitness function that quantitatively evaluates the quality of each candidate privacy budget allocation. The optimization problem of this invention is formalized as minimizing this fitness function, which is formally defined as follows:

[0090] (15); The fitness function is obtained by weighting the mean relative error (ARE), the Kullback-Leibler divergence (KLD), and the normalization penalty term adjusted for the order of the Hilbert curve. The specific expression is as follows: (16); in, For the fitness function, This is a normalization penalty term for adjusting the order of the Hilbert curve. The order of the Hilbert curve Adjustments It is the total privacy budget. It is a privacy budget allocation strategy at the prefix tree level. It is the pruning threshold. This represents the threshold parameter.

[0091] Mean Relative Error (ARE) quantifies the accuracy of point estimation and is widely used in range and point queries. A lower ARE indicates higher accuracy. Kullback-Leibler Divergence (KLD) measures the difference between two probability distributions. In trajectory publishing tasks, it evaluates the distributional similarity between synthetic trajectories and original user trajectory data; a smaller value means closer similarity. It is a normalization penalty for adjusting the order of the Hilbert curve. Original design and equivalence class size Related, .actual It must be a positive integer and should not be less than [a certain value]. This theoretical lower bound ensures complete spatial coverage. Therefore, It is considered an adjustable variable to maximize the overall data utility.

[0092] 2. Adaptive Neighborhood Quantity: In the traditional FDA algorithm, the neighborhood quantity is a fixed parameter. However, this fixed setting may limit the algorithm's performance in certain situations. For example, when the fitness of the current solution is low, the probability of generating neighborhoods with higher fitness decreases significantly, i.e., fitness is positively correlated with the number of generated neighborhoods. Therefore, this invention proposes an adaptive neighborhood quantity method that dynamically adjusts the number of generated neighborhoods based on the evaluated fitness. The specific formula is as follows:

[0093] (20); in, MaxSize It is the maximum value of the number of neighbors. It is a constant to prevent division by zero errors. It is the number of neighborhoods. It represents the fitness of the worst-fitting individual in the current water flow population. It refers to the size of the water flow population. It is the first The adaptability of the water flow It is the first The location of the water flow is determined. In this way, solutions with higher fitness will generate more neighborhoods, while solutions with lower fitness will generate fewer neighborhoods. This adaptive strategy helps reduce oscillations around local optima during the optimization process, thereby improving optimization efficiency.

[0094] 3. Parallelization: Although FDA, as a heuristic algorithm, can provide a satisfactory solution within a finite time, its efficiency still has room for improvement. To further improve the efficiency of the algorithm, this invention proposes a parallelization architecture based on Spark. Spark is a big data processing framework designed specifically for distributed clusters, which can effectively accelerate the processing of large-scale data.

[0095] In traditional heuristic parallelization design, all critical steps are typically parallelized. However, this design is not entirely suitable for the optimization task of this invention. Analysis revealed that the fitness calculation portion of the FDA algorithm consumes a significant portion of the runtime. As the population size increases, the fitness calculation time also increases significantly. Therefore, this invention specifically designs a parallelization strategy for the fitness function, as shown in Algorithm 2.

[0096] Algorithm 2: SP-IFDA Parallelization Design: Input: Population size Npop, maximum number of iterations Spark cluster parameters conf; Output: Optimal parameter set The specific processing steps are as follows:

[0097] Create a SparkContext object sc using conf; generate Npop initial solutions pop; convert pop to RDD data format RDDpop using sc.parallelize(); compute the fitness function of each solution in RDDpop in parallel using map(getFitness()); sort the fitness results and return listfitness using collect(); tmp = 0.

[0098] While tmp ≥ do: renew Find the neighboring Neighbors; convert Neighbors to RDD data format RDDpop using sc.paralleize(); compute the fitness function of each solution in RDDpop in parallel using map(getFitness()); sort the fitness results and return listfitness using collect(); update pop based on listfitness and FDA update strategy; convert pop to RDD data format RDDpop using sc.paralleize(); compute the fitness function of each solution in RDDpop in parallel using map(getFitness()); sort the fitness results and return listfitness using collect(); find the minimum value fitnessbest in listfitness; tmp = tmp + 1.

[0099] End while: Decode the solution best corresponding to fitnessbest as... End algorithm.

[0100] First, the initial solutions to be evaluated are converted into Spark Resilient Distributed Dataset (RDD) format by calling the `sc.parallelize()` function. Then, based on the Spark Resilient Distributed Dataset (RDD), the fitness of each solution is computed in parallel using the `map()` function. Finally, the fitness results are aggregated and collected at the master node using the `collect()` function to obtain the fitness of all water flows. This parallel design significantly reduces the time spent on fitness computation, thereby improving the overall efficiency of the algorithm. The flowchart of SP-IFDA is as follows: Figure 4 As shown.

[0101] Step 3.4: When the fitness of the best neighborhood is less than the fitness of the current flow, generate a random number and move the current flow to the random number of best flows. Re-evaluate the fitness of the flows, select the best flow, and use the updated flow position as the optimal parameter combination.

[0102] Step 4: Perform noise addition and pruning operations on the original user trajectory data with the optimal parameter combination to generate and publish the final user trajectory data.

[0103] The above process will be demonstrated through experiments below: The proposed optimization method, SP-IFDA, is implemented using Python 3.7.1 and evaluated on the T-Drive dataset released by Microsoft Research Asia. This dataset contains GPS trajectory data of approximately 10,357 Beijing taxis over a period of one week. The size of the preprocessed dataset is shown in Table 1.

[0104] Table 1. Preprocessed dataset Following the coding and evaluation process of the benchmark study, each parameter configuration was run 10 times, and the arithmetic mean was taken to comprehensively evaluate the performance improvement brought about by the proposed optimization strategy.

[0105] This experiment mainly focuses on the following four research questions: RQ1: Is SP-IFDA the best heuristic algorithm for optimizing the parameter configuration of formula (15)? RQ2: Can SP-IFDA improve computational efficiency through parallelization? RQ3: Under different prefix tree heights h, what advantages does SP-IFDA-Traj have compared to the benchmark method and GAPBAS? RQ4: Has SP-IFDA-Traj reached the current state-of-the-art (SOTA) level? 1) In the convergence experiment (RQ1), due to the limitation of the "no free lunch" theorem, this invention cannot directly specify a particular heuristic algorithm as optimal. Therefore, this invention verifies its advantages in parameter optimization problems by comparing the convergence performance of SP-IFDA with nine mainstream heuristic algorithms. The algorithms compared include: FDA, GA, PSO, Differential Evolution (DE), GWO, Whale Optimization Algorithm (WOA), Sine Cosine Algorithm (SCA), Chicken Swarm Optimization (CSO), and Biogeography-Based Optimization (BBO).

[0106] The population size for all algorithms was set to 5, the maximum number of iterations was 20, and each algorithm was run independently 5 times. The number of neighbors between FDA and SP-IFDA was set to 8. The experimental results are shown in Tables 2 and 3.

[0107] Table 2. Convergence test results for the BJ-Day3 dataset. Table 3. Convergence test results for the BJ-Day7 dataset. It can be seen that the average fitness of FDA is better than other traditional heuristic algorithms, validating the motivation for improving it in this invention. The average fitness of SP-IFDA is approximately 52.9% higher than FDA (1.74% improvement on BJ-Day 3 and 103.98% improvement on BJ-Day 7), indicating stronger convergence ability. The standard deviations of all algorithms are within acceptable ranges, demonstrating that SP-IFDA has a significant advantage in parameter optimization problems. Figure 5 (a) and Figure 5 (b) shows the changing trends of the optimal fitness curves on BJ-Day3 and BJ-Day7, respectively.

[0108] 2) In the scalability experiment (RQ2): To evaluate the scalability of SP-IFDA in a large-scale distributed environment, this invention conducted a series of experiments based on the cluster resources provided by the Beijing High-Performance Computing Center. The experimental environment covered single-node (independent operation) and Spark local cluster modes with 2, 4, and 8 nodes to simulate multi-node distributed computing scenarios. This mode can reproduce multi-node behavior on a single multi-core CPU, facilitating the evaluation of the algorithm's time overhead and speedup performance under different resource configurations. The Spark parameters were configured as follows: each executor was allocated 2GB of memory and 1 CPU core, and the driver was configured with 1GB of memory and 1 core. Each node was allocated resources independently, and the experimental parameters did not affect the final conclusions.

[0109] (1) Strong scalability: Strong scalability refers to improving performance by increasing the number of processors while keeping the problem size unchanged. Figure 6 (a) and Figure 6 Figure (b) shows the trends in runtime and speedup of SP-IFDA under different population sizes. The results indicate that computational overhead increases with population size. When the computational load is small, the speedup effect is not significant due to the overhead of Spark clusters in task startup and resource scheduling; however, as the computational task gradually increases, the parallel advantages of SP-IFDA become increasingly apparent, and the speedup gradually approaches the theoretical optimal value, demonstrating good scalability.

[0110] (2) Weak scalability: Weak scalability refers to increasing the number of nodes while keeping the computational workload of each node constant, and observing the change in overall efficiency. The experimental results are shown in Table 4.

[0111] Table 4. Experimental Results of Weak Scalability It can be seen that as the number of nodes increases, the growth rate of SP-IFDA's time overhead is lower than the growth rate of its computational complexity, indicating that it has a certain degree of weak scalability in a distributed environment and is suitable for large-scale parameter optimization tasks.

[0112] 3) In the tree height impact and comparative evaluation (RQ3 & RQ4), to analyze the impact of prefix tree height on overall performance and to verify the advantages of SP-IFDA compared to the benchmark method and GAPBAS, this invention designed a set of comparative experiments. Experimental setup We then performed two representative prefix queries (hBs and hBs@) on the BJ-Day3 and BJ-Day7 datasets, using ARE as the evaluation metric.

[0113] Figure 7 Figures (a)–7(d) illustrate the trend of ARE variation under different tree heights. It can be seen that, under all tree height configurations, the ARE of SP-IFDA is significantly lower than that of the baseline method and GAPBAS, indicating its stronger search capability and stability in parameter optimization. Even in finer-grained hBs@ queries, SP-IFDA maintains the lowest error and exhibits minimal fluctuation under different tree heights, demonstrating good robustness of its optimization results to structural changes. Furthermore, the baseline method uses fixed parameters, resulting in smaller performance variations under different tree heights; GAPBAS, although using a genetic algorithm for optimization, is sensitive to changes in tree height, leading to significant ARE fluctuations; while SP-IFDA not only achieves better error control but also maintains stability comparable to the fixed-parameter method, further validating the effectiveness and practicality of its optimization strategy. In summary, extensive experiments on large-scale real-world trajectory datasets demonstrate that SP-IFDA-Traj significantly improves the trade-off between privacy and utility: its optimization engine achieves an average fitness improvement of approximately 52.9% over the original FDA in convergence tests. In terms of trajectory query accuracy, its error is significantly reduced to 1% of the baseline method and only 10% of other existing optimization strategy models.

[0114] This invention addresses the issue of fitness evaluation taking up a significant portion of time. It enables high-quality solutions to obtain more sufficient local search resources and reduces invalid computations for low-quality solutions, thereby reducing oscillations of the algorithm near local optima. It automatically adjusts the parameters of personalized noise prefix tree trajectory publishing, significantly improving the trade-off between privacy and utility and promoting the advancement of practical differential privacy trajectory publishing.

[0115] Based on the above, the present invention provides a differential privacy trajectory publishing system, comprising: a data acquisition module, an identification module, an optimization module, and a final publishing module.

[0116] The system comprises the following modules: a data acquisition module to acquire raw user trajectory data that satisfies differential privacy; an identification module to identify the set of key parameters affecting the raw user trajectory data, including the Hilbert curve order, total privacy budget, prefix tree hierarchical privacy budget allocation strategy, and pruning threshold; an optimization module to jointly optimize the set of key parameters using an improved flow direction algorithm, aiming to minimize a predefined fitness function and obtain the optimal parameter combination; the improved flow direction algorithm is based on the original flow direction algorithm, introducing chaotic mapping initialization for initializing the set of key parameters, introducing an adaptive neighborhood generation mechanism to dynamically adjust the number of neighborhoods for the fitness of individual water flow, and using Spark-based parallel fitness calculation to obtain fitness; and a final publishing module to perform noise addition and pruning operations on the raw user trajectory data with the optimal parameter combination, generating and publishing the final user trajectory data.

[0117] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a program, and when the program is executed by the processor, the processor performs the steps of a differential privacy trajectory publishing method.

[0118] According to the disclosed embodiments, the computer device can communicate with one or more external devices (e.g., keyboard, pointing device, Bluetooth communication, etc.) or with any device that enables the computing device to communicate with one or more other computing devices (e.g., router, demodulator, etc.).

[0119] The present invention also provides a storage medium storing a computer program thereon, characterized in that the computer program, when executed by a processor, implements the steps of a differential privacy trajectory publishing method.

[0120] According to the disclosed embodiments, the storage medium can be a non-volatile computer-readable storage medium, such as, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, the storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0121] The above description, in conjunction with specific preferred embodiments, provides a more detailed explanation of the present invention. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention.

Claims

1. A differential privacy trajectory publishing method, characterized in that, Including the following steps: Obtain raw user trajectory data that satisfies differential privacy; Identify a set of key parameters that affect the original user trajectory data; the set of key parameters includes: Hilbert curve order, total privacy budget, prefix tree hierarchical privacy budget allocation strategy, and pruning threshold. The improved flow direction algorithm performs joint optimization of the key parameter set to minimize the predefined fitness function and obtain the optimal parameter combination. The improved flow direction algorithm is based on the original flow direction algorithm, introduces chaotic mapping initialization for initializing the key parameter set, introduces an adaptive neighborhood generation mechanism to dynamically adjust the number of neighborhoods for the fitness of individual water flow, and obtains fitness through parallel fitness calculation based on Spark. The original user trajectory data is subjected to noise addition and pruning operations with the optimal parameter combination to generate and publish the final user trajectory data.

2. The differential privacy trajectory publishing method as described in claim 1, characterized in that, The improved flow direction algorithm is used to jointly optimize the set of key parameters, aiming to minimize the predefined fitness function and obtain the optimal parameter combination. Specifically: Determine the initial set of key parameters; The initial key parameter set is processed using chaotic mapping to generate an initial solution; wherein, each set of parameters in the initial key parameter set corresponds to an initial solution in the flow direction algorithm, i.e., a water flow; With the goal of minimizing the predefined fitness function, the fitness of the water flow is evaluated for each initial solution based on the parallel fitness computation of Spark. The evaluated fitness is used to generate an adaptive neighborhood, and the fitness of the water flow is evaluated again after the adaptive neighborhood is generated to select the best neighborhood. When the fitness of the best neighborhood is less than the fitness of the current flow, a random number is generated, and the current flow is directed to the random number of best flows. The fitness of the flows is evaluated again, the best flow is selected, and the updated flow position is used as the optimal parameter combination.

3. The differential privacy trajectory publishing method as described in claim 2, characterized in that, The objective of minimizing the predefined fitness function is specifically as follows: The fitness function is obtained by weighting the mean relative error (ARE), the Kullback-Leibler divergence (KLD), and the normalization penalty term adjusted for the order of the Hilbert curve. The specific expression is as follows: ； To obtain the minimum predefined fitness function, the specific expression is: ； in, For the fitness function, This is a normalization penalty term for adjusting the order of the Hilbert curve. The order of the Hilbert curve Adjustments It is the total privacy budget. It is a privacy budget allocation strategy at the prefix tree level. It is the pruning threshold. This represents the threshold parameter.

4. The differential privacy trajectory publishing method as described in claim 2, characterized in that, The adaptive neighborhood generation based on the evaluated fitness is specifically as follows: The number of generated neighborhoods is dynamically adjusted based on the evaluated fitness; fitness is positively correlated with the number of generated neighborhoods, as shown in the following expression: ； in, MaxSize It is the maximum value of the number of neighbors. It is a constant. It is the number of neighborhoods. It represents the fitness of the worst-fitting individual in the current water flow population. It refers to the size of the water flow population. It is the first The adaptability of the water flow It is the first The location of the water flow.

5. The differential privacy trajectory publishing method as described in claim 2, characterized in that, The Spark-based parallel fitness computation evaluates the fitness of the water flow for each initial solution, specifically as follows: Transform the initial solution to be evaluated into a Spark Resilient Distributed Dataset RDD; Based on Spark Resilient Distributed Dataset (RDD), the fitness of each initial solution is obtained in parallel, and the obtained fitness results are summarized to obtain the fitness of all water flows.

6. The differential privacy trajectory publishing method as described in claim 1, characterized in that, The acquisition of raw user trajectory data that satisfies differential privacy specifically involves: The collected raw user trajectory data is grouped under spatiotemporal constraints to construct several trajectory equivalence classes; For the spatial distribution of points within each trajectory equivalence class, the optimal Hilbert order is selected, and representative points are selected from the trajectory equivalence class. The Hilbert curve is traversed under the optimal Hilbert order, and the geographical coordinates of the traversed representative points are converted into one-dimensional strings using the staggered position rule. Insert a one-dimensional string into the prefix tree, add noise to the count values ​​stored in the prefix tree, and allocate a preset privacy budget to the prefix tree; Based on a preset pruning threshold, the prefix tree after the privacy budget allocation is pruned to generate original user trajectory data that satisfies differential privacy.

7. The differential privacy trajectory publishing method as described in claim 6, characterized in that, When performing spatiotemporal constraint grouping on the collected raw user trajectory data, the raw user trajectory data whose start and end timestamp deviations are both within the threshold are grouped into different trajectory equivalence classes.

8. A differential privacy trajectory publishing system, characterized in that, include: The data acquisition module is used to acquire raw user trajectory data that satisfies differential privacy. The identification module is used to identify a set of key parameters that affect the original user trajectory data; The set of key parameters includes: Hilbert curve order, total privacy budget, prefix tree hierarchical privacy budget allocation strategy, and pruning threshold; The optimization module is used to jointly optimize the set of key parameters through an improved flow direction algorithm, with the goal of minimizing the predefined fitness function to obtain the optimal parameter combination. The improved flow direction algorithm is based on the original flow direction algorithm, introduces chaotic mapping initialization for initializing the set of key parameters, introduces an adaptive neighborhood generation mechanism to dynamically adjust the number of neighborhoods for the fitness of individual water flow, and obtains fitness through parallel fitness calculation based on Spark. The final publishing module is used to perform noise addition and pruning operations on the original user trajectory data with the optimal parameter combination to generate and publish the final user trajectory data.

9. A computer device, characterized in that, The device includes a memory and a processor, wherein the memory stores a program that, when executed by the processor, causes the processor to perform the steps of a differential privacy trajectory publishing method as described in any one of claims 1 to 7.

10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of a differential privacy trajectory publishing method according to any one of claims 1 to 7.

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