A sparse social network influence maximization method and device based on multi-layer graph contraction and reverse reachable graph sampling

Abstract

This invention discloses a method and apparatus for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling. First, the original graph is contracted layer by layer to obtain a smaller thumbnail with a similar structure. Then, an influence maximization algorithm is applied to the thumbnail to obtain an approximate set of seed nodes. Finally, the thumbnail is expanded layer by layer to restore the original graph, while the seed node set is expanded and optimized layer by layer to push information on topics of interest to users. Compared with existing algorithms in the field of influence maximization, this invention can effectively solve sparse social networks with a huge number of nodes. By contracting, it increases the density of the graph structure and solves the problems of excessive locality in single sampling and weak overall coverage of the graph structure in traditional reverse reachability graph sampling algorithms, thereby significantly reducing the time and space overhead required for sampling. Furthermore, this invention has the advantages of simple implementation, good approximation ability, and strong scalability.

Description

Technical Field

[0001] This invention relates to the field of graph data computation in social networks, and in particular to a method and apparatus for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling. Background Technology

[0002] Since the beginning of the Internet era, how to select the most suitable online influencers within a limited budget in order to maximize the reach of information has become an application problem of concern to businesses, governments, and academia.

[0003] Thus, the problem of maximizing influence arises: by modeling the social network as a directed graph structure G(V,E), each user is considered a node; no more than k nodes are selected as seed nodes for information, so that under the independent cascading diffusion model, the information can spread to as many nodes as possible from the seed nodes. Backward reachability graph sampling has become the mainstream algorithm for solving the maximization problem: each sampling randomly selects a central node v, and performs a random backward breadth-first search around it; the search range characterizes the influence of surrounding nodes on v. However, contemporary social networks, represented by online social platforms, often have a huge number of nodes (10... 8 10 9 The sparse distribution of edges in giant graphs (mega-graphs) means that the activity range of most users is limited to a small circle of a few people. Traditional reverse reachability graph sampling methods for processing giant graphs consume too much time and storage space. Furthermore, for such sparse graphs, a single sampling may cover too localized an area, causing the algorithm to rely on more sampling iterations to ensure a good overall solution, further worsening the time and space overhead. This invention provides a simple, well-applied, and highly scalable solution to the problem of maximizing the influence of giant graph structures. By shrinking the graph structure layer by layer, a smaller and denser thumbnail is obtained, and the reverse reachability graph sampling algorithm is used to solve the problem on the thumbnail, thus overcoming the aforementioned drawbacks of traditional algorithms. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method and apparatus for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling. This method is used to solve the problem of maximizing the influence of social networks, that is, selecting information seed nodes to maximize the propagation range of information.

[0005] The objective of this invention is achieved through the following technical solution: Firstly, this invention provides a method for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling. The specific steps of this method are as follows:

[0006] (1) Obtain the directed graph G(V,E) of the online social platform, the weight c(v) of each user node, the propagation probability p(u,v) of each user's interested topic information, the number of seed nodes k, and the graph shrinkage threshold n. c The seed nodes are influential users on online social platforms.

[0007] (2) Introducing the "seed probability" p s (u,v) represents the probability that information will successfully propagate from user u to other users v when user u is set as the seed node; for each directed edge (u,v)∈E representing the attention relationship between users in the directed graph G, let p s (u,v)←p(u,v);

[0008] (3) Shrink the directed graph G(V,E): Let the shrinking level t←0, and the original graph be denoted as G0(V0,E0); repeat the following steps until |V t |≤n c : G t-1 Merge the nodes into an undirected graph, perform a graph matching algorithm on the merged undirected graph, group each user node, and merge and shrink the user nodes in each group to form G. t For each user node, calculate the estimated in-degree and out-degree of each user node before shrinkage, and calculate G. t Construct G using the weights of user nodes in the middle and the weights of bidirectional edges between user nodes before merging. t (V t E t Then let t←t+1;

[0009] (4) For thumbnail G t (V t E t Find the initial solution to obtain the initial seed node set. |S C |≤k;

[0010] (5) Expand the thumbnail and optimize the seed nodes layer by layer during the expansion process to obtain the seed node set S0 of the directed graph G, and push the topic information that users are interested in.

[0011] Furthermore, the specific process of step (3) is as follows:

[0012] 3.1 Let the shrinkage level t←0, and the original graph be denoted as G0(V0,e0);

[0013] 3.2 If |V t |≤n c If the condition is met, this step ends and proceed to step 4; otherwise, proceed to step 3.3.

[0014] 3.3 G t-1 Merge into an undirected graph For G t-1 (V t-1 E t-1 Each directed edge (u,v) ∈ E represents a follow relationship between users. t-1 Add the undirected edge (u,v) to the edge set of the undirected graph. If its reverse edge (v,u)∈E t-1 If it exists, the weight of the undirected edge is the larger of p(u,v) and p(v,u); otherwise, the weight of the undirected edge is p(u,v).

[0015] 3.4 The undirected graph obtained by merging Execute the graph matching algorithm to match each user node u∈V t-1 Group into groups; let n be the groupings. t To determine the number of groups, let π(u) ∈ {1 … n} t} represents user node u∈V t-1 Group numbering; construct the next layer of user node set V t All user nodes with π(u) = i in the upper layer shrink to a single user node v′ in the lower layer. i ∈V t , i = 1 … n t ;make This indicates that all elements in the previous layer have shrunk to v′. i The set of user nodes;

[0016] 3.5 Calculate the value of each user node u∈V before shrinkage. t-1 in-degree estimate d in (u) and the out-degree estimate d out (u);

[0017] 3.6 For each merged user node v′ i ∈V t Calculate the point weight c(v′) after merging. i );

[0018] 3.7 Let the next layer be the set of directed edges representing the attention relationships between users. For any two merged user nodes v′ i ,v′ j ∈V t If there exists a bidirectional edge (u) before the merge i ,u j )∈E t-1 Make Let E t ←E t ∪{(v′ i,v′ j )}, and calculate its edge weight p(v′) i ,v′ j ) and p s (v′ i ,v′ j );

[0019] 3.8 Building the next layer of online social platforms: Social Network G t (V t E t );

[0020] 3.9 Let t←t+1, then return to step 3.2.

[0021] Furthermore, the specific process of step (4) is as follows:

[0022] 4.1 Set the number of samplings q, and let the sampling set...

[0023] 4.2 If If so, proceed to step 4.11; otherwise, proceed to step 4.3.

[0024] 4.3 Randomly select a central node v i ∈V t The probability of it being selected is c(v). i ) / C, where For graph G t The total weight of all nodes in the process;

[0025] 4.4 Let queue Q ← {v i Let the set R that has been traversed be... i ←{v i},R Q ←{v i};

[0026] 4.5 If the queue is empty, proceed to step 4.9; otherwise, proceed to step 4.6.

[0027] 4.6 Remove the head node v from queue Q vur ;

[0028] 4.7 Traversing v cur Each incoming edge (u,v) cur ): Get a random number x uniformly distributed in the range [0,1). If x <p s (u,v cur Let R i ←R i ∪{u}; if x <p(u,v cur )and Then add u to the end of queue Q, and let R... Q←R Q ∪{u};

[0029] 4.8 Proceed to step 4.5;

[0030] Order 4.9

[0031] 4.10 Proceed to step 4.2;

[0032] 4.11 Let the seed node set

[0033] 4.12 If |S t |=k or |S t |=|V t If |, then end this step and return. Otherwise proceed to step 4.13;

[0034] 4.13 Select a new seed node in Let x be a predicate function, which is defined when proposition x is true. When x is false

[0035] 4.14 Order S t ←S t ∪{s * Proceed to step 4.12.

[0036] Furthermore, the specific process of step (5) is as follows:

[0037] 5.1 Let S t The output of step 4 is the current expanded level t′←t;

[0038] 5.2 If t′<0, then end this step; otherwise, proceed to step 5.3;

[0039] 5.3 Order S t′-1 ←{SelectBestSeed(s)|s∈S t′}; SelectBestSeed(s) means selecting the optimal seed node s, so that the pushed topic information of interest to the user starts from this seed node and is pushed through S. t′ The estimated outflow was then the largest.

[0040] 5.4 Let t′←t′-1, then return to step 5.2.

[0041] Secondly, the present invention also provides a device for maximizing the influence of a social network based on multi-layer graph shrinkage and reverse reachability graph sampling, including a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it implements the method for maximizing the influence of a sparse social network based on multi-layer graph shrinkage and reverse reachability graph sampling.

[0042] Thirdly, the present invention also provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the method for maximizing the influence of a sparse social network based on multi-layer graph contraction and reverse reachability graph sampling.

[0043] Fourthly, the present invention also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the aforementioned method for maximizing the influence of a sparse social network based on multi-layer graph contraction and reverse reachability graph sampling.

[0044] The beneficial effects of this invention are as follows: Compared with existing algorithms in the influence maximization domain, this invention can effectively solve sparse social networks with a huge number of nodes. By shrinking, it increases the density of the graph structure and solves the problems of excessive locality of a single sampling and weak overall coverage of the graph structure in traditional reverse reachable graph sampling algorithms. This significantly reduces the time and space overhead required for sampling. At the same time, this invention has the advantages of simple implementation, good approximation ability, and strong scalability. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of the process framework of the method of the present invention;

[0047] Figure 2 A schematic diagram of the flowchart framework for the graph shrinkage algorithm at each layer;

[0048] Figure 3 This diagram illustrates the impact of the in-degree estimate on the edge weights after the contraction process.

[0049] Figure 4 This is a structural diagram of a sparse social network influence maximization device based on multi-layer graph contraction and reverse reachability graph sampling according to the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the invention.

[0051] This invention proposes a method for maximizing the influence of sparse social networks based on multi-level graph shrinkage and reverse reachability graph sampling. The method obtains parameters such as the directed graph G(V,E) of online social networks like Weibo and Twitter, the weight c(v) of each user node, the information propagation probability p(u,v) of each edge representing the follow relationship between users, and the specified number of seed nodes k. By performing a multi-level graph segmentation algorithm on the social network G(V,E), it shrinks layer by layer to a smaller, structurally similar thumbnail G. C (V C E C Then, perform any influence maximization algorithm on the thumbnail to obtain a set of seed nodes for the thumbnails. Finally, the thumbnail is expanded layer by layer to restore the original image G(V,E). During the expansion process, the seed nodes are optimized to obtain a set of information seed nodes for this social network. |S|=k, which maximizes the expected range of push propagation (the total weight of the nodes receiving the information) of the topic that the user is interested in, starting from the seed node and under the independent cascading model.

[0052] The method (Cw-IM) of this invention is as follows: Figure 1 As shown, it includes the following steps:

[0053] 1. Obtain the directed simple graph G(V,E) of the social network, the weight c(v) of each user node, the propagation probability p(u,v) of each topic information that a user is interested in, the number of seed nodes k, and the graph shrinkage threshold n. c Algorithm parameters such as sampling number q; graph shrinkage threshold n c Determined based on experience. Experiments show that n c =n / 200 is a relatively balanced parameter setting for most sparse social networks. At this setting, the algorithm can achieve an approximation ratio of over 95% while significantly reducing time and space overhead. A lower graph shrinkage threshold can further compress the algorithm's time and space overhead, but there is a risk that the solution performance will deteriorate significantly.

[0054] 2. Introduce the "seed probability" p s (u,v) represents the probability that information will successfully propagate from user node u to user node v when user node u is set as the seed node. For each directed edge (u,v)∈E representing a relationship of interest between users, let p s (u,v)←p(u,v);

[0055] 3. Shrink the original image G(V,E) layer by layer to obtain the thumbnail G. t (V t E t ), such that |V t |≤n c Where t is G c The shrinkage level (the original image's level is 0), V t Represents thumbnail G t The set of user nodes in the graph; the graph shrinking process in this step, the flow is as follows: Figure 2 As shown, the details are as follows:

[0056] 3.1 Let the shrinkage level t←0, and the original graph be denoted as G0(V0,E0);

[0057] 3.2 If |V t |≤n c If the condition is met, this step ends and proceed to step 4; otherwise, proceed to step 3.3.

[0058] 3.3 G t-1 Merge into an undirected graph For G t-1 (V t-1 E t-1 Each directed edge (u,v) ∈ E represents a follow relationship between users. t-1 Add the undirected edge (u,v) to the edge set of the undirected graph. If its reverse edge (v,u)∈E t-1 If it exists, the weight of the undirected edge is the larger of p(u,v) and p(v,u); otherwise, the weight of the undirected edge is p(u,v).

[0059] 3.4 The undirected graph obtained by merging Execute the graph matching algorithm to match each user node u∈V t-1 Group the data. Let n be the group. t The number of groups obtained depends on the specific graph matching algorithm used, let π(u)∈{1 … n t} represents user node u∈V t-1 Group numbering; construct the next layer of user node set V t All user nodes with π(u) = i in the upper layer shrink to a single user node v′ in the lower layer. i ∈V t , i = 1 … n t .make This indicates that all elements in the previous layer have shrunk to v′. i The set of user nodes;

[0060] 3.5 Calculate the value of each user node u∈V before shrinkage. t-1 in-degree estimate d in (u) and the out-degree estimate d out (u);

[0061] 3.6 For each merged user node v′ i ∈V t Calculate the point weight c(v′) after merging. i );

[0062] 3.7 Let the next layer be the set of directed edges representing the attention relationships between users. For any two merged user nodes v′ i ,v′ j ∈V t If there exists a bidirectional edge (u) before the merge i ,u j )∈E t-1 Make Let E t ←E t ∪{(v′ i ,v′ j )}, and calculate its edge weight p(v′) i ,v′ j ) and p s (v′ i ,v′ j );

[0063] 3.8 Building the next layer of online social platforms: Social Network G t (V t E t );

[0064] 3.9 Let t←t+1, then return to step 3.2.

[0065] 4. For thumbnail G t (V t E t Find the initial solution to obtain the initial seed node set. |S t |≤k; The specific steps are as follows:

[0066] 4.1 Let the sampling set

[0067] 4.2 If If so, proceed to step 4.11; otherwise, proceed to step 4.3.

[0068] 4.3 Randomly select a central node v i ∈V t The probability of it being selected is c(v).i ) / C, where For graph G t The total weight of all nodes in the process;

[0069] 4.4 Let queue Q ← {v i Let the set R that has been traversed be... i ←{v i},R Q ←{v i};

[0070] 4.5 If the queue is empty, proceed to step 4.9; otherwise, proceed to step 4.6.

[0071] 4.6 Remove the head node v from queue Q cur ;

[0072] 4.7 Traversing v cur Each incoming edge (u,v) cur ): Get a random number x uniformly distributed in the range [0,1). If x <p s (u,v cur Let R i ←R i ∪{u}; if x <p(u,v cur )and Then add u to the end of queue Q, and let R... Q ←R Q ∪{u};

[0073] 4.8 Proceed to step 4.5;

[0074] Order 4.9

[0075] 4.10 Proceed to step 4.2;

[0076] 4.11 Let the seed node set

[0077] 4.12 If |S t |=k or |S t |=|V t If |, then end this step and return. Otherwise proceed to step 4.13;

[0078] 4.13 Select a new seed node in Let x be a predicate function, which is defined when proposition x is true. When x is false

[0079] 4.14 Order S t ←S t ∪{s *Proceed to step 4.12.

[0080] 5. Expand the thumbnail layer by layer, and optimize the seed nodes layer by layer during the expansion process to obtain the seed node set S0 of the original image; the specific steps are as follows:

[0081] 5.1 Let S t The output of step 4 is the current expanded level t′←t;

[0082] 5.2 If t′<0, then end this step; otherwise, proceed to step 5.3;

[0083] 5.3 Order S t′-1 ←{SelectBestSeed(s)|s∈S t′};

[0084] 5.4 Let t′←t′-1, then return to step 5.2.

[0085] 6. Output S0 as the seed node set for the algorithm solution. Based on the obtained seed node set, push topic information that users are interested in.

[0086] The graph matching algorithm in step 3.4 can be any existing undirected graph matching algorithm. Neighbor maximal matching is the simplest implementation; for each unmatched user node, it is paired with the unmatched node with the largest neighbor edge weight from its neighbors. However, considering that most social networks are power-law graphs, using only neighbor maximal matching might result in a large number of nodes near "hotspots" (i.e., nodes with high degree) remaining unmatched and forming separate groups, thus increasing the total number of groups n. t The problem arises when the number of nodes is too high, severely compromising graph shrinkage efficiency. One solution is to introduce a "sibling pairing" strategy. After a maximum neighbor match, all unmatched neighbors of each node are checked, and every two unmatched neighbors form a new sibling pairing, such that the number of pairs n... t This allowed for significant compression.

[0087] The in-degree estimate d in step 3.5 ib (u) is defined as the sum of the weights p(x,u) of all incoming edges (x,u) of u, excluding all incoming neighbors that are in the same group as user u, where x represents the user node connected to u by an incoming edge; the out-degree estimate d out (u) is defined as the sum of the weights p(u,y) of all outgoing edges (u,y) of u, excluding all outgoing neighbors of the same group as user u, where y represents the user node connected to u by an outgoing edge. Figure 3 For example, since u1 has more neighboring edges passing information to it compared to u2, d in (u1)>d in(u2) When merging point weights and edge weights, more consideration is given to the influence of information flowing in from u1.

[0088]

[0089]

[0090] For each user node v after shrinkage i ′∈V t Calculate each node before shrinkage Normalized in-degree estimate h I (u i ):make If Σd in (v i If ′)=0 then h I (u i h = 0; otherwise h I (u i )=d in (u i ) / Σd in (v i ′).

[0091] In step 3.6, the point weight c(v) i The merging method of ′) is defined as follows: This represents the probability that a topic of interest to a user, originating from a single non-seed node 'a', transiting through several nodes in node S, and finally reaching any user node in node set B. Enumerate each user node. pass Approximate estimate of information flowing in from any inlet Inside, it will pass through u j The probability size.

[0092]

[0093] In step 3.7, the edge weight p(v) i ′,v j The merging method of ′) is defined as follows: enumerate information inflow Every entrance Calculation information from user u i Departure, via Arriving after transiting through other nodes The probability of any node in the array, and using h I (u i As information from u i An approximate estimate of the inflow probability.

[0094]

[0095] In step 3.7, the additional edge weight p s (v i ′,v j The merging method of ′) is defined as follows: This represents the probability that information originates from a single seed node a, passes through several nodes in S, and then reaches any user node in the point set B. First, select... The optimal seed node, SelectBestSeed(v′), is selected internally so that the pushed topic information of interest to the user originates from this seed node and proceeds through... The estimated outflow is then maximized; then the information is calculated starting from that seed node, via... transit arrival The probability of any user node in the system.

[0096]

[0097]

[0098] In steps 3.6 and 3.7, a∈S is specified. and The exact values ​​of CalculateP(SB,{a},{a},B,0) and CalculateP(SB,{a},{a},B,1) can be calculated using dynamic programming.

[0099] CalculateP(S,T,A,B,F) means that, given the following conditions, ... and Let T be the set of nodes that have received information, and A be the set of nodes that received information in the previous round. The probability of information reaching any node in B if it continues to propagate from A is given. A flag F=0 indicates that A is a non-seed node set, and F=1 indicates that A is a seed node set. The dynamic programming algorithm steps are as follows:

[0100] 1) Input S, T, A, B, and limit... and Input the flag bit F, if the calculation Then F = 0, if we calculate Then F = 1;

[0101] 2) Let p1←AtLeastOne(A,B,F);

[0102] 3) Let r ← 0; let Let ST be the set of all non-empty subsets of ST;

[0103] 4) If Then proceed to step 10); otherwise proceed to step 5.

[0104] 5) Take make

[0105] 6) Order

[0106] 7) Let y0←1-AtLeastOne(A,STA) next ,F);

[0107] 8) Let r←r+y1y0×CalculateP(S,T∪A) next A next ,B,0);

[0108] 9) Proceed to step 4);

[0109] 10) Return p1+(1-p1)r as the result.

[0110] Where AtLeastOne(A,B,F) represents the probability that information originates from the seed node set (F=1) or the non-seed node set (F=0) and, after one round of propagation, at least one node in B successfully receives the information.

[0111]

[0112]

[0113] In step 2) of the dynamic programming algorithm, p1 represents the probability that information reaches B from A in the current round; otherwise, steps 3)-9) enumerate all possible cases A of the information reaching the node in the current round. next And in the next round from A next The algorithm is then recursively implemented. y1 represents the information propagated from A to A in the current round. next The probability of each node in the algorithm, where y0 represents the information starting from A and not reaching A in the current round. next The probability of any node other than A. In step 9), since A next It is not a set of seed nodes, so the flag is forced to be F=0.

[0114] Step 4's initial solution process employs the concept of "reverse reachability graph sampling." For random sampling (R... i ,v i This indicates that information can be propagated to the target node v in this sampling. i The set of all seed nodes R i That is: if s∈R i If s is set as the seed node, then user v i Information on topics of interest can be propagated to v during this sampling. i Therefore, for each node s∈Vt The more times something appears in the sampling, the more target nodes the information can propagate to, starting from the seed node s. When the central node v... i The probability of being selected is proportional to its weight c(v) i When ), it can be proven that obtaining a sufficient number of samples {(R)} i ,v i After )|i=1 … q}, the seed node set S t Total number of sampling coverage This is an approximate estimate of the objective function for the weighted influence maximization problem. Since F(S) t )and Both satisfy monotonicity and submodularity, therefore A greedy algorithm can be used to obtain an approximate solution with an approximation ratio of 1-1 / e (corresponding to steps 4.11 to 4.14 above).

[0115] Example: This invention uses the Weibo online social platform as an example to push topic information of interest to users, to explain the specific implementation scheme of the invention. The specific process is as follows:

[0116] 1. Obtain the directed social network graph G(V,E) of Weibo, the weight c(v) of each user node, and the seed probability p of each topic that a user is interested in. s (u,v), and the number of seed nodes k, graph shrinkage threshold n c Parameters such as sampling number q; among which seed nodes are verified big V bloggers and core users with a high number of followers, and other user nodes are ordinary users, and the edges between user nodes represent the follow relationship between users;

[0117] 2. Weibo, an online social platform, has a massive user base with a sparse user distribution. The vast majority of users' activities are confined to a small circle of a handful of people. The method designed in this invention shrinks the directed graph of Weibo's social network layer by layer, resulting in a smaller and denser thumbnail G. t (V t E t ), such that |V t |≤n c Where t is G c The shrinkage level (the original image's level is 0), V t Represents thumbnail G t The set of user nodes in;

[0118] 3. For thumbnail G t (V t E t Find the initial solution to obtain the initial seed node set. |S t|≤k;

[0119] 4. Expand the thumbnail layer by layer, and optimize the seed nodes layer by layer during the expansion process to obtain the seed node set S0 of the original image; including influential bloggers and users with a high number of followers, these users are all highly influential users; based on the obtained seed node set, push information on topics that users are interested in, and use the "influencer effect" to achieve the goal of widespread publicity and expand the scope of information dissemination as much as possible.

[0120] Corresponding to the aforementioned embodiment of a method for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling, the present invention also provides an embodiment of a device for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling.

[0121] See Figure 4 The present invention provides a device for maximizing the influence of a sparse social network based on multi-layer graph shrinkage and reverse reachability graph sampling, comprising a memory and one or more processors. The memory stores executable code, and when the processor executes the executable code, it is used to implement a method for maximizing the influence of a sparse social network based on multi-layer graph shrinkage and reverse reachability graph sampling as described in the above embodiment.

[0122] The embodiment of the sparse social network influence maximization device based on multi-layer graph contraction and reverse reachability graph sampling provided by this invention can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 4 The diagram shown is a hardware structure diagram of any data processing-capable device that can be used to maximize the influence of a sparse social network based on multi-layer graph contraction and reverse reachability graph sampling, as provided by the present invention. (Except for...) Figure 4 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0123] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0124] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0125] This invention also provides a computer-readable storage medium storing a program that, when executed by a processor, implements a method for maximizing the influence of a sparse social network based on multi-layer graph shrinkage and reverse reachability graph sampling as described in the above embodiments.

[0126] The computer-readable storage medium can be an internal storage unit of any data processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device of any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of any data processing device. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0127] The present invention also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the aforementioned method for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling.

[0128] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A sparse social network influence maximization method based on multi-layer graph contraction and reverse reachable graph sampling, characterized in that, The specific steps of this method are as follows: (1) obtaining a directed graph of an online social platform , a weight of each user node , a propagation probability of each piece of user interested topic information , and a number of seed nodes and a graph contraction threshold ; the seed nodes are users with influence in the online social platform (2) Introducing "seed probability" Indicates when user When set as a seed node, information is obtained from the user. To other users The probability of successful propagation; for directed graphs Each edge represents a directed edge indicating a follow relationship between users. ,make ; (3) on directed graphs contraction: let the contraction level , the original graph is recorded as ; Repeat the following steps until :Will Merge the nodes into an undirected graph, perform a graph matching algorithm on the merged undirected graph, group each user node, and merge and shrink the user nodes in each group to form a single undirected graph. For each user node, calculate the estimated in-degree and out-degree before shrinking. Construct the user node weights and the edge weights of the bidirectional edges between user nodes before merging. Then let The specific process is as follows: 3.1 Shrinkage hierarchy , the original drawing is marked ; 3.2 If then end the step and perform step 4; otherwise, go to step 3.

3. 3.3 Add to the edge set of the undirected graph : for each directed edge in the directed graph representing a follow relationship between users , add an undirected edge to the edge set of the undirected graph ; if its reverse edge exists, then the weight of the undirected edge is taken to be the greater of and ; otherwise, the weight of the undirected edge is ; 3.4 The undirected graph obtained by merging Execute the graph matching algorithm to match each user node Grouping; Record Let be the number of groups obtained by grouping. Represents user node Group numbering; constructing the user node set for the next layer. All of the above layers The user nodes shrink to a single user node in the next layer. , ;make This indicates that all elements in the previous layer have shrunk to... The set of user nodes; 3.5 Calculate the number of user nodes before shrinkage in-degree estimate and exit degree estimate ; 3.6 For each merged user node Calculate the point weights after merging. ; 3.7 Let the set of directed edges in the next layer represent the attention relationships between users. For any two merged user nodes If there exists a bidirectional edge before the merge Make Then let And calculate its edge weights. and ; 3.8 Building a social network for the next layer of online social platforms ; 3.9 Order Return to step 3.2; (4) Thumbnails Find the initial solution to obtain the initial seed node set. ; (5) Expand the thumbnail and optimize the seed nodes layer by layer during the expansion process to obtain a directed graph. seed node set To push information on topics that users are interested in.

2. The method for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling according to claim 1, characterized in that, The specific process of step (4) is as follows: 4.1 Set the number of samples Let the sampling set ; 4.2 If If yes, proceed to step 4.11; otherwise, proceed to step 4.

3. 4.3 Randomly select a central node The probability of it being selected is ,in For the image The total weight of all nodes in the process; 4.4 Let the queue Let the set that has been traversed be... ; 4.5 If the queue is empty, proceed to step 4.9; Otherwise proceed to step 4.6; 4.6 From the queue Remove the first node from the team ; 4.7 Traversal Each incoming edge : Get Uniformly distributed random numbers within a range ,like Then let ;like and Then Add to queue At the end, and let ; 4.8 Proceed to step 4.5; 4.9 Order ; 4.10 Proceed to step 4.2; 4.11 Let the set of seed nodes be... ; 4.12 If or Then end this step and return. Otherwise, proceed to step 4.13; 4.13 Select a new seed node ,in As a predicate function, when the proposition When true , When it is false ; 4.14 Order Proceed to step 4.

12.

3. The method for maximizing the influence of sparse social networks based on multi-layer graph contraction and reverse reachability graph sampling according to claim 1, characterized in that, The specific process of step (5) is as follows: 5.1 Order The current expanded level is the output of step 4. ; 5.2 If If so, then this step ends; Otherwise proceed to step 5.3; 5.3 Order ; This indicates the selection of the optimal seed node. This ensures that the pushed information about topics that users are interested in originates from this seed node, and then... The estimated outflow was then the largest. 5.4 Order Return to step 5.

2.

4. A device for maximizing the influence of a sparse social network based on multi-layer graph shrinkage and reverse reachability graph sampling, comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements a method for maximizing the influence of sparse social networks based on multi-layer graph shrinkage and reverse reachability graph sampling as described in any one of claims 1-3.

5. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements a method for maximizing the influence of sparse social networks based on multi-layer graph shrinkage and reverse reachability graph sampling as described in any one of claims 1-3.

6. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement a method for maximizing the influence of a sparse social network based on multi-layer graph contraction and reverse reachability graph sampling as described in any one of claims 1-3.

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