Complementary and competitive independent cascade model social network influence maximization algorithm

Abstract

The present invention relates to a complementary and competitive independent cascade model social network influence maximization algorithm, comprising: specifying priorities of four types of information, Ca+, Ca, Cr and Cr-, according to input parameters; determining a sub-algorithm on the basis of monotonicity and sub-modularity of the priorities of the four types of information, sub-algorithms comprising a PR-IMM sub-algorithm, an SA-IMM sub-algorithm and an SA-RG-IMM sub-algorithm. Beneficial effects of the present invention are: the present invention provides a unified universal framework for commonly observed coexistence of positive information maximization and negative information minimization; on the basis of an independent cascade model for information dissemination, insofar as a positive information seed node is known, a specified number of "information enhancement nodes" are provided to increase dissemination capacity of the positive information as much as possible; insofar as a negative information seed node is known, a specified number of "information enhancement nodes" are provided to prevent negative information dissemination as much as possible.

Description

A collaborative-competitive social network influence maximization algorithm under an independent cascade model Technical Field

[0001] The present invention relates to the technical field of social network influence propagation, and more specifically, to a social network influence maximization algorithm with both collaboration and competition under an independent cascade model. Background Art

[0002] With the rapid development of internet information, maximizing the spread of specific types of information (or minimizing negative public opinion such as rumors and hate speech) has become a research topic of interest to governments, businesses, and social science researchers. A social network can be viewed as a mathematical graph structure G(V,E), where each node v∈V represents an actor in the social network, such as a company, a public account, or an end user. Each directed edge e=(v1,v2)∈E represents an information transmission relationship, meaning that node v1 has a certain probability of directly transmitting the information to v2. The classic influence maximization problem aims to select a limited number of nodes in a social network as information sources, or "seed nodes," to ensure that information from these nodes spreads as widely as possible. Another research approach assumes that the information source is known and fixed, and selects several "enhancing nodes" to polish the received information, enhancing its spread (increasing the probability of transmission along each edge). Regarding the negative information minimization problem, given a known negative information source, a limited number of suppressor nodes are selected to block the spread of negative information, thereby minimizing the number of recipients of the information. It can be proven that both of these problems are NP-hard. The above existing studies are all limited to one of the two application problems: maximizing positive information or minimizing negative information, and have not yet involved the situation where positive and negative information are co-disseminated and compete with each other in the public opinion field.

[0003] Summary of the Invention

[0004] The purpose of the present invention is to address the deficiencies of the existing technology and propose a social network influence maximization algorithm with both collaboration and competition under an independent cascade model.

[0005] First, we provide a collaborative-competitive social network influence maximization algorithm under an independent cascade model, including:

[0006] S1. Specify the priorities of four types of information, Ca+, Ca, Cr, and Cr-, based on the input parameters. Ca and Cr represent the positive and negative information, respectively, spread by the information seed node before passing through the enhancement node. Ca+ represents the enhanced positive information with greater spreadability after passing through the enhancement node. Cr- represents the weakened negative information with less harmfulness after passing through the enhancement node.

[0007] S2. Determine a sub-algorithm according to the monotonicity and sub-modularity of the four types of information priorities, wherein the sub-algorithm includes a PR-IMM sub-algorithm, a SA-IMM sub-algorithm, and a SA-RG-IMM sub-algorithm.

[0008] Preferably, S2 includes:

[0009] S201, if monotonicity and submodularity are satisfied, execute the PR-IMM subalgorithm;

[0010] S202, if only monotonicity is satisfied but submodularity is not satisfied, then execute the SA-IMM subalgorithm;

[0011] S203: In other cases, execute the SA-RG-IMM sub-algorithm.

[0012] Preferably, in S201, the PR-IMM sub-algorithm includes:

[0013] S2011, perform multiple reverse reachable graph sampling in the input graph structure: for the i-th sampling, a central node v is randomly selected with equal probability in the graph i , from v i Start a breadth-first search along the reverse edge of the graph structure to obtain the sampled subgraph R i For each node u, if it is set as a separate enhanced node, it can be the central node v i The benefit value g(u;R i ,v i );

[0014] S2012, the influence maximization problem is equivalent to the set covering problem: select a specified number k of enhanced nodes u1...u in the graph k , the contribution of the enhanced node to each node v in the social network is recorded as Where R, v represents a random reverse reachable graph sampling and its randomly selected central node; solve the objective function

[0015] S2013, using the sampling results of S2011 as the expectation The estimated value of; let the total number of sampling be θ, take Where R1...R θ is the subgraph obtained by sampling, v1...v θ is the central node randomly selected for each sampling; based on the above approximate estimate and the monotone submodularity of the problem, a greedy algorithm is used to solve the equivalent set cover problem of S2012, and the optimal enhanced nodes u1...u are selected one by one. k .

[0016] Preferably, in S202, the SA-IMM sub-algorithm includes:

[0017] S2021, assume that the information priority is Ca+>Cr->Cr>Ca, and execute the PR-IMM sub-algorithm based on this priority to obtain a set of solutions for the enhanced node

[0018] S2022. Enumerate each node in the graph as the central node v for sampling the reverse reachable graph, perform θ sampling on each node v, and take As The estimate of , that is, the benefit value brought to v after node u is set as a separate enhanced node;

[0019] S2023. The lower bound of the problem is approximately equivalent to the set cover problem of monotone submodules: select a specified number k of enhanced nodes u1...u k , for each node v, enhance the lower bound of the node's cumulative contribution to v Solving the objective function

[0020] S2024. Based on the estimated value of S2022, use the greedy algorithm to solve the lower bound equivalence problem of S2023 to obtain another set of solutions for the enhanced nodes.

[0021] S2025. Compare the two sets of solutions obtained in S2021 and S2024, estimate the actual benefits of the two sets of solutions as enhanced nodes in the social network by simulating the information propagation process, and take the better set of solutions as the output of the sub-algorithm.

[0022] Preferably, in S203, the SA-RG-IMM sub-algorithm includes:

[0023] S2031, assume that the information priority is Ca+>Cr->Cr>Ca, execute the PR-IMM sub-algorithm based on the priority to obtain a set of solutions for the enhanced node

[0024] S2032, enumerate each node in the graph as the central node v of the reverse reachable graph sampling, perform θ sampling on each node v, and take As The estimate of , that is, the benefit value brought to v after node u is set as a separate enhanced node;

[0025] S2033. The lower bound of the problem is approximately equivalent to the set cover problem of monotone submodules: select a specified number k of enhanced nodes u1...u k , for each node v, enhance the lower bound of the node's cumulative contribution to v Solving the objective function

[0026] S2034. Based on the estimated value of S2032, use the randomized greedy algorithm to solve the lower bound equivalence problem of S2023 to obtain another set of solutions for the enhanced nodes.

[0027] S2035. Compare the two sets of solutions obtained in S2031 and S2034, estimate the actual benefits of the two sets of solutions as enhanced nodes in the social network by simulating the information propagation process, and take the better set of solutions as the output of the sub-algorithm.

[0028] As an advantage, the PR-IMM sub-algorithm and the SA-IMM sub-algorithm can be The probability of obtaining an approximate optimal solution with an approximate ratio of 1-1 / e-∈; SA-RG-IMM can The probability of obtaining an approximate optimal solution with an approximate ratio of 1 / e-∈; where e=2.71828... is a natural constant, |V| is the total number of nodes in the social network graph, Parameters defined by the user.

[0029] In a second aspect, a system for maximizing social network influence with both collaboration and competition under an independent cascade model is provided, which is configured to execute the algorithm for maximizing social network influence with both collaboration and competition under any independent cascade model described in the first aspect, including:

[0030] The designation module is used to specify the priorities of four types of information, Ca+, Ca, Cr, and Cr-, based on input parameters. Ca and Cr represent the positive and negative information disseminated by the information seed node before passing through the enhancement node, respectively. Ca+ represents the enhanced positive information with greater dissemination ability after passing through the enhancement node. Cr- represents the weakened negative information with less harmfulness after passing through the enhancement node.

[0031] The determination module is used to determine the sub-algorithm according to the monotonicity and sub-modularity of the four types of information priorities, and the sub-algorithm includes the PR-IMM sub-algorithm, the SA-IMM sub-algorithm and the SA-RG-IMM sub-algorithm.

[0032] In a third aspect, a computer storage medium is provided, wherein a computer program is stored in the computer storage medium; when the computer program is executed on a computer, the computer executes the social network influence maximization algorithm with both cooperation and competition under any independent cascade model described in the first aspect.

[0033] The beneficial effects of the present invention are as follows: the present invention provides a unified general framework for the common situation of maximizing positive information and minimizing negative information. Based on the independent cascade model of information propagation, the present invention simultaneously handles the weighted average of the following two sub-problems with a theoretical approximation ratio of up to 1-1 / e-∈: (1) Given the positive information seed nodes, a specified number of "information enhancement nodes" are set to maximize the propagation capacity of positive information; (2) Given the negative information seed nodes, a specified number of "information enhancement nodes" are set to minimize the spread of negative information. Furthermore, the present invention is applicable to various situations where the relative priority of positive and negative information is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flow chart of the C2-IC algorithm process;

[0035] Figure 2 is a flow chart of the PR-IMM sub-algorithm;

[0036] Figure 3 is a flow chart of the SA-IMM and SA-RG-IMM sub-algorithms;

[0037] Figure 4 is a schematic diagram of the relationship between information propagation priority and the monotonicity and submodularity of the objective function. DETAILED DESCRIPTION

[0038] The present invention will be further described below with reference to the following examples. The following examples are provided only to facilitate understanding of the present invention. It should be noted that, without departing from the principles of the present invention, it is possible for a person skilled in the art to make various modifications to the present invention, and such improvements and modifications fall within the scope of the claims of the present invention.

[0039] Example 1:

[0040] The Independent Cascade Model (IC) is a popular discrete diffusion model currently used in the study of influence propagation. It simplifies the information propagation process into a series of discrete moments t = 0, 1, 2, ... In the Independent Cascade Model (IC), each edge e = (v1, v2) ∈ E has a weight p(e) representing the probability that node v1, after receiving the information at a certain moment t, will successfully propagate it to node v2 at the next moment t+1. For "enhanced node" research problems, another probability value p is set for each edge. + (e)≥p(e) represents the probability of propagation of enhanced information along this edge.

[0041] This application selects a series of "enhanced nodes" to collaboratively enhance the dissemination of positive information while "neutralizing" the negative information that has passed through the enhanced nodes. This allows the neutral information to still be disseminated but not harmful, thereby competing with the negative information. Through reduction, it can be proved that the collaborative-competitive impact maximization problem is NP-Hard. Depending on the relative priority of positive and negative information, the monotonicity and submodularity of this problem exist in three cases: (1) monotonic submodular, (2) monotonic but non-submodular, and (3) non-monotonic and non-submodular.

[0042] For the above three situations, the C2-IC algorithm is divided into three sub-algorithms: (1) PR-IMM, (2) SA-IMM and (3) SA-RG-IMM. All of the above sub-algorithms have been proven to be The probability of obtaining an approximate optimal solution with an approximate ratio of 1-1 / e-∈ (for PR-IMM and SA-IMM) or 1 / e-∈ (for SA-RG-IMM), where |V| is the total number of nodes in the social network graph, Parameters defined by the user.

[0043] Specifically, in the PR-IMM sub-algorithm, if it is necessary to satisfy the following theoretically: The probability of obtaining a solution with an approximation ratio of 1-1 / e-∈ is as follows: the greedy approximation ratio δ = 1-1 / e, the number of nodes n = |V|, α, β are intermediate variables; the number of sampling nodes The total number of sampling times required for the i-th sampling node is N i , the objective function threshold is S i (N i With S i The specific meaning and use of , see S2011, i = 1...q); sampling lower bound function See S2014 for details; see S2016 for details of the final sampling frequency function Θ(S). Another feasible practical solution is to take the number of sampling nodes q = 1, that is, fixed sampling times, in which case the sampling frequency N can be set arbitrarily according to actual needs. Can be ignored.

[0044] For the SA-IMM algorithm, if it is necessary to satisfy the following theoretically: The probability of obtaining a solution with an approximation ratio of 1-1 / e-∈ is 1-1 / e-∈. The parameters in the sub-algorithm are as follows: the number of nodes n = |V|, κ is an intermediate variable, Θ(κ) is a fixed function of κ, and the number of samples taken from each central node is θ (for details on its meaning and use, see S2023). If runtime is limited, users can also customize parameters such as θ to control the algorithm's runtime. θ←Θ(κ)

[0045] For the SA-RG-IMM algorithm, if it is necessary to satisfy the following theoretically: The probability of obtaining a solution with an approximation ratio of 1 / e-∈ is as follows, the parameters in the sub-algorithm are as follows, where the number of nodes n = |V|, the intermediate variable κ is as follows, and the expression of the function Θ(κ) is the same as above; the number of samples for each central node is θ (see S2033 for its specific meaning and use): θ←Θ(κ)

[0046] The information designed by the C2-IC algorithm model is divided into four categories: Ca+, Ca, Cr, and Cr-. The original positive information Ca and the original negative information Cr are both sent by their respective seed nodes (known in advance as the input of the algorithm), and are continuously propagated based on the independent cascade model. The propagation success rate on each edge e∈E is p(e). When the original positive information Ca reaches the enhancement node, the enhancement node will change it into the enhanced positive information Ca+, and its propagation success rate is increased to p + (e)≥p(e); When the original negative information Cr reaches the enhancement node, the enhancement node will change it into harmless neutral information Cr-, so that it can participate in the dissemination competition and squeeze the dissemination ability of the negative information Cr.

[0047] For the C2-IC algorithm, given the number of enhanced nodes k∈N + , weight parameter λ∈[0,1], the objective function is defined as:

[0048] in Indicates that at the enhanced nodes u1...u k The expected number of nodes receiving positive information (including Ca and Ca+) under the influence of represents the expected number of nodes that receive negative information Cr. That is, the contribution of each Ca or Ca+ node to the objective function is λ, the contribution of each Cr node is -(1-λ), and the contribution of each Cr- node and all other nodes that do not receive any information is 0.

[0049] Specifically, the collaborative-competitive social network influence maximization algorithm under the independent cascade model proposed in the embodiment of the present application combines the two sub-problems of maximizing enhanced information and minimizing negative information in a weighted average manner, as shown in Figure 1, including:

[0050] S1. Specify the priorities of the four types of information Ca+, Ca, Cr, and Cr- according to the input parameters.

[0051] Specifically, Ca and Cr represent the positive and negative information disseminated by the information seed node before passing through the enhancement node, respectively; Ca+ represents the enhanced positive information with greater dissemination ability after passing through the enhancement node; Cr- represents the weakened negative information with less harmfulness after passing through the enhancement node.

[0052] If the objective function F(u1...u k ) satisfies monotonicity, then M=1, otherwise M=0; if F(u1...u k ) satisfies the submodularity, then S = 1, otherwise S = 0;

[0053] S2. Determine sub-algorithms based on the monotonicity and sub-modularity of the four types of information priorities. The sub-algorithms include PR-IMM sub-algorithm, SA-IMM sub-algorithm, and SA-RG-IMM sub-algorithm.

[0054] Specifically, S2 includes:

[0055] S201. If monotonicity and submodularity are satisfied, i.e., M=1 and S=1, then execute the PR-IMM subalgorithm;

[0056] S202. If only monotonicity is satisfied but submodularity is not satisfied, that is, M = 1 and S = 0, then execute the SA-IMM subalgorithm;

[0057] S203: In other cases, execute the SA-RG-IMM sub-algorithm.

[0058] The present embodiment is described using four types of information priorities that satisfy monotonicity and submodularity. As shown in FIG2 , the PR-IMM sub-algorithm includes:

[0059] S2011, propose several sampling times nodes N1 <N2<...<N q , and the objective function thresholds S1...S q , let N0 = 0. Definition is the set of all currently acquired reverse reachable graph samples, initially Define loop variable i←1; define sampling lower bound value L←1;

[0060] S2012: If i≤q, proceed to S2013; otherwise proceed to S2016;

[0061] S2013, Execute N i -N i-1 Reverse reachable graph sampling: Each sampling randomly selects a central node v with equal probability in the graph j , from v j Start with a breadth-first search in the reverse graph, that is, on the basis of the original graph, each directed edge e∈E takes the opposite direction, p(e) and p + (e) remains unchanged. Within the scope of breadth-first search, after obtaining each node u as a separate enhanced node, under the fixed edge sampling state, the node v j The objective function contribution g j (u;R j ,v j ). Take the result of breadth-first search as a sample and add it to the set After this step is completed

[0062] S2014, according to the sampling set at this time Try a greedy algorithm to obtain the objective function value S of the local optimal solution at this time. If S≥S i , then let in The sampling lower bound function pre-specified for the algorithm; then jump to S2016;

[0063] S2015, let i←i+1, jump to S2012;

[0064] S2016, let the final sampling number θ = Θ (L), where Θ (L) is the final sampling number function pre-specified by the algorithm. Continue the sampling process and add the set After this step is completed

[0065] S2017, according to the sampling set at this time Execute the last greedy algorithm to obtain the local optimal solution u1...u of the enhanced node k As the output of the algorithm.

[0066] In the PR-IMM sub-algorithm, set the sampling number nodes N1...N q The purpose is: for each node N i And the objective function value S of S2014 at this node, if it can be theoretically proved that when S≥S i When the theoretical approximation ratio is satisfied, the algorithm can jump to S2016, which can reduce a large number of unnecessary sampling times and greatly save algorithm time. and the final sampling frequency function Θ(L) is input by the user The equal error parameter is determined by appropriate settings so that the algorithm process can ensure the approximation ratio of 1-1 / e-∈ while the theoretically required number of sampling times is as small as possible.

[0067] In the greedy algorithms of the PR-IMM subalgorithms S2014 and S2017, due to the monotone submodularity of the objective function, it can be proved that the classical greedy algorithm can obtain a theoretical approximate solution to the equivalent set cover problem with a 1-1 / e approximation ratio: if in the jth sampling, the node u is relative to the central node v of the sampling j Satisfy g(u;R j ,v j )>0, it can be considered that node u is g(u; R j ,v j )'s weight "covers" the sample R j After equivalently converting to the set cover problem, each time greedily select a node that can make the objective function increment optimal, add it to the output list and update the increments of the remaining candidate nodes; repeat the above process k times to obtain the enhanced node list u1...u k .

[0068] In addition, the specific steps of the sampling mentioned above are as follows:

[0069] Step 1: Randomly select a central node v with equal probability in the graph;

[0070] Step 2: Randomly assign the state of this sampling to all edges in the graph according to their respective probabilities: For each edge e∈E, it has a probability p(e) of being fixed as an active state, p + The probability of (e)-p(e) is fixed to the enhanced state, 1-p + The probability of (e) is fixed to the blocked state;

[0071] Step 3: Create a breadth-first search queue Q←{v} and sample the subgraph point set V R ←{v};

[0072] Step 4: If the queue Q is empty at this time, jump to step (7); otherwise, execute step (5);

[0073] Step 5. Remove the node u at the head of the queue from Q. Traverse all edges that reach u: For each edge (x,u)∈E, if the incoming neighbor And the edge (x,u) is in the active or enhanced state, then let Q←Q∪{x},V R ←V R ∪{x};

[0074] Step 6: Jump to step (4) to continue the breadth-first search process;

[0075] Step 7: Sample the edge set E of the subgraph R ←{(x,y)∈E|x∈V R ∧y∈V R}, construct the sampling subgraph R←G(V R ,E R );

[0076] Step 8: If V R If there is no seed node in , set g(u; R, v) = 0 for all nodes u in this sampling and end this sampling process; otherwise, execute step (9);

[0077] Step 9. Simulate the forward propagation of information in the sampled subgraph R: positive and negative information start from the seed nodes sampled in the subgraph respectively, simulate the information propagation process based on the linear threshold model, and record the weight δ of the central node v after the propagation is completed: if the node v receives the information Ca, then δ←λ; if the node v receives the information Cr, then δ←-(1-λ); in other cases, δ←0;

[0078] Step 10. For each node u in the sampled subgraph, calculate the contribution value g(u; R, v): If u is a seed node or u = v, then g(u; R, v) = 0. Otherwise, set u as the only augmented node in the subgraph. Simulate the information propagation process again and obtain the weight δ′ of the central node v after the end. If node v receives information Ca or Ca+, then δ′←λ; if node v receives information Cr, then δ′←-(1-λ); otherwise, δ←0. Set g(u; R, v) = δ′-δ.

[0079] Example 2:

[0080] Based on Example 1, Example 2 of the present application provides another social network influence maximization algorithm with both collaboration and competition under an independent cascade model, including:

[0081] S1. Specify the priorities of the four types of information Ca+, Ca, Cr, and Cr- according to the input parameters.

[0082] S2. Determine sub-algorithms based on the monotonicity and sub-modularity of the four types of information priorities. The sub-algorithms include PR-IMM sub-algorithm, SA-IMM sub-algorithm, and SA-RG-IMM sub-algorithm.

[0083] Specifically, S2 includes:

[0084] S201. If monotonicity and submodularity are satisfied, i.e., M=1 and S=1, then execute the PR-IMM subalgorithm;

[0085] S202. If only monotonicity is satisfied but submodularity is not satisfied, that is, M = 1 and S = 0, then execute the SA-IMM subalgorithm;

[0086] S203: In other cases, execute the SA-RG-IMM sub-algorithm.

[0087] The embodiment of the present application is described as follows: four types of information priorities satisfy monotonicity but do not satisfy submodularity. As shown in FIG3 , the SA-IMM subalgorithm includes:

[0088] S2021, assume that the information priority is Ca+>Cr->Cr>Ca, and execute the PR-IMM sub-algorithm based on this priority to obtain a set of solutions for the enhanced node

[0089] S2022. Select any node v in the graph that has not been selected as a central node before. If all nodes have been selected as central nodes, jump to S2034; otherwise, execute step S2033.

[0090] S2023, perform θ times of reverse reachability graph sampling with v as the center: each sampling R j Starting from v, a breadth-first search is performed in the reverse graph, that is, on the basis of the original graph, each directed edge e∈E takes the reverse direction, p(e) and p + (e) remains unchanged. Within the scope of breadth-first search, after obtaining each node u as a separate enhancement node, under this fixed edge sampling state, the contribution value g(u; R j ,v). For each node u∈V in the graph, let

[0091] S2024, jump to S2022 to continue sampling;

[0092] S2025, μ obtained from S2022 to S2024 u,v ,u,v∈V, execute the greedy algorithm to solve the objective function F(u1...u k )'s lower bound H (LB) (u1...u k ) to obtain the local optimal solution, where The results of the greedy algorithm are used as another set of solutions for the enhanced nodes.

[0093] S2026. Simulate the two solutions obtained in S2021 and S2025 separately. That is, simulate the information propagation process after adding the enhanced nodes in the graph and obtain the estimation of the objective function through the Monte Carlo method. Take the solution with the higher estimated value as the output u1...u k .

[0094] The SA-IMM algorithm uses a simplified version of the "sandwich method" non-submodular objective function, that is, the upper bound and lower bound objective functions are solved separately, and then the better one is selected from the two sets of solutions.

[0095] In S2021, the result of executing the PR-IMM sub-algorithm with information priority Ca+>Cr->Cr>Ca is taken as the objective function F(u1...u k ). It can be verified that, for all priority relationships among the four types of information described above, the objective function value at this priority level is always no lower than that of all other priorities under the same conditions. Figure 1 shows that the objective function at this priority level satisfies monotonicity and submodularity, making it suitable for the PR-IMM subalgorithm.

[0096] The lower bound function H in S2025 (LB) (u1...u k ) can be proved to have monotone submodularity, so the greedy algorithm can also be used to obtain the local optimal solution of the equivalent matrix covering problem with a 1-1 / e approximation ratio: define the matrix N n×n ={μ u,v} u∈V,v∈V , select k rows in the matrix to color, then for each column, take the maximum weight of all the colored grids in the column as the benefit of the column, and solve the problem of maximizing the total benefit of all columns. Each time, greedily select a row u with the largest benefit increment after coloring i And update the selected maximum weight of each column of the matrix, and perform k iterative greedy solutions.

[0097] It should be noted that the parts in this embodiment that are the same or similar to those in Example 1 can be referenced to each other and will not be described in detail in this application.

[0098] Example 3:

[0099] Based on Example 1, Example 3 of the present application provides another social network influence maximization algorithm with both collaboration and competition under an independent cascade model, including:

[0100] S1. Specify the priorities of the four types of information Ca+, Ca, Cr, and Cr- according to the input parameters.

[0101] S2. Determine sub-algorithms based on the monotonicity and sub-modularity of the four types of information priorities. The sub-algorithms include PR-IMM sub-algorithm, SA-IMM sub-algorithm, and SA-RG-IMM sub-algorithm.

[0102] Specifically, S2 includes:

[0103] S201. If monotonicity and submodularity are satisfied, i.e., M=1 and S=1, then execute the PR-IMM subalgorithm;

[0104] S202. If only monotonicity is satisfied but submodularity is not satisfied, that is, M = 1 and S = 0, then execute the SA-IMM subalgorithm;

[0105] S203: In other cases, execute the SA-RG-IMM sub-algorithm.

[0106] The embodiment of the present application is described as follows: the priority of four types of information does not satisfy monotonicity and does not satisfy submodularity. As shown in FIG3 , the SA-RG-IMM sub-algorithm includes:

[0107] S2031, assume that the information priority is Ca+>Cr->Cr>Ca, execute the PR-IMM sub-algorithm based on the priority to obtain a set of solutions for the enhanced node

[0108] S2032. Select any node v in the graph that has not been selected as a central node before. If all nodes have been selected as central nodes, jump to S2034; otherwise, execute step S2033.

[0109] S2033, perform v times of reverse reachability graph sampling with v as the center: each sampling R j Starting from v, a breadth-first search is performed in the reverse graph, that is, on the basis of the original graph, each directed edge e∈E takes the reverse direction, p(e) and p + (e) remains unchanged. Within the scope of breadth-first search, after obtaining each node u as a separate enhancement node, under this fixed edge sampling state, the contribution value g(u; R j ,v). For each node u∈V in the graph, let

[0110] S2034, jump to S2022 to continue sampling;

[0111] S2035, μ obtained from S2032 to S2034 u,v ,u,v∈V, execute the random greedy algorithm to the objective function F(u1...u k ) Obtain the local optimal solution and use the result of the random greedy algorithm as another set of solutions for the enhanced nodes

[0112] S2036: Simulate the two solutions obtained in S2031 and S2035 respectively. That is, simulate the information propagation process after adding the enhanced nodes in the graph and obtain the estimation of the objective function through the Monte Carlo method. The solution with the higher estimated value is taken as the output of the algorithm u1...u k .

[0113] The biggest difference between the SA-RG-IMM subalgorithm and the SA-IMM subalgorithm is that the former uses a "random greedy" strategy, which ensures an approximate solution to the non-monotonic but submodular subproblem. When , we obtain a theoretical approximation ratio of 1 / e-∈. In the randomized greedy algorithm, in each iteration, one of the k options with the largest incremental benefit is randomly selected with equal probability and added to the list output by the algorithm.

[0114] It should be noted that the parts in this embodiment that are the same or similar to those in Example 1 can be referenced to each other and will not be described in detail in this application.

[0115] Example 4:

[0116] Based on Example 1, Example 4 of the present application provides a social network influence maximization system with both collaboration and competition under an independent cascade model, including:

[0117] The designation module is used to specify the priorities of four types of information, Ca+, Ca, Cr, and Cr-, based on input parameters. Ca and Cr represent the positive and negative information disseminated by the information seed node before passing through the enhancement node, respectively. Ca+ represents the enhanced positive information with greater dissemination ability after passing through the enhancement node. Cr- represents the weakened negative information with less harmfulness after passing through the enhancement node.

[0118] The determination module is used to determine the sub-algorithm according to the monotonicity and sub-modularity of the four types of information priorities, and the sub-algorithm includes the PR-IMM sub-algorithm, the SA-IMM sub-algorithm and the SA-RG-IMM sub-algorithm.

[0119] Specifically, the system provided in this embodiment is a system corresponding to the method provided in Example 1. Therefore, the parts in this embodiment that are the same or similar to those in Example 1 can be referenced to each other and will not be repeated in this application.

Claims

1. A collaborative-competitive social network influence maximization algorithm under an independent cascade model, characterized by: include: S1. Specify the priorities of four types of information Ca+, Ca, Cr and Cr- according to the input parameters; Among them, Ca and Cr represent the positive and negative information spread by the information seed node before passing through the enhancement node, respectively; Ca+ represents the enhanced positive information with stronger dissemination ability after passing through the enhancement node; Cr- represents the weakened negative information with lower dissemination harm after passing through the enhancement node; S2. Determine a sub-algorithm according to the monotonicity and sub-modularity of the four types of information priorities, wherein the sub-algorithm includes a PR-IMM sub-algorithm, a SA-IMM sub-algorithm and a SA-RG-IMM sub-algorithm.

2. The collaborative-competitive social network influence maximization algorithm under the independent cascade model according to claim 1, characterized in that S2 include: S201, if monotonicity and submodularity are satisfied, execute the PR-IMM subalgorithm; S202, if only monotonicity is satisfied but submodularity is not satisfied, then execute the SA-IMM subalgorithm; S203. In other cases, execute the SA-RG-IMM sub-algorithm.

3. The social network influence maximization algorithm with both collaboration and competition under the independent cascade model according to claim 2 is characterized in that: In S201, the PR-IMM sub-algorithm includes: S2011, perform multiple reverse reachable graph sampling in the input graph structure: for the i-th sampling, a central node v is randomly selected with equal probability in the graph i , from v i Start a breadth-first search along the reverse edge of the graph structure to obtain the sampled subgraph R i For each node u, if it is set as a separate enhanced node, it can be the central node v i The benefit value g(u; R i ,v i ); S2012. The influence maximization problem is equivalent to the set covering problem: select a specified number k of enhanced nodes u1...u in the graph k , the contribution of the enhanced node to each node v in the social network is recorded as Where R, v represents a random reverse reachable graph sampling and its randomly selected central node; solve the objective function S2013, using the sampling results of S2011 as the expectation The estimated value of; let the total number of sampling be θ, take Where R1...R θ is the subgraph obtained by sampling, v1...v θ is the central node randomly selected for each sampling; based on the above approximate estimate and the monotone submodularity of the problem, a greedy algorithm is used to solve the equivalent set cover problem of S2012, and the optimal enhanced nodes u1...u are selected one by one. k .

4. The social network influence maximization algorithm with both collaboration and competition under the independent cascade model according to claim 3 is characterized in that: In S202, the SA-IMM sub-algorithm includes: S2021, assuming that the information priority is Ca+>Cr->Cr>Ca, and executing the PR-IMM sub-algorithm based on the priority to obtain a set of solutions for the enhanced node S2022. Enumerate each node in the graph as the central node v for sampling the reverse reachable graph, sample each node v θ times, and take As The estimate of is the benefit value that node u brings to v after setting it as a separate enhanced node; S2023. The lower bound of the problem is approximately equivalent to the set covering problem of monotone submodules: select a specified number k of enhanced nodes u1...u k , for each node v, enhance the lower bound of the node's cumulative contribution to v Solving the objective function S2024. Based on the estimated value of S2022, use the greedy algorithm to solve the lower bound equivalent problem of S2023 to obtain another set of solutions for the enhanced nodes. S2025. Compare the two sets of solutions obtained in S2021 and S2024, estimate the actual benefits of the two sets of solutions as enhanced nodes in the social network by simulating the information propagation process, and take the better set of solutions as the output of the sub-algorithm.

5. The social network influence maximization algorithm with both collaboration and competition under the independent cascade model according to claim 4 is characterized in that: In S203, the SA-RG-IMM sub-algorithm includes: S2031, assuming that the information priority is Ca+>Cr->Cr>Ca, and executing the PR-IMM sub-algorithm based on the priority to obtain a set of solutions for the enhanced node S2032, enumerate each node in the graph as the central node v of the reverse reachable graph sampling, sample each node v θ times, and take As The estimate of is the benefit value that node u brings to v after setting it as a separate enhanced node; S2033. The lower bound of the problem is approximately equivalent to the set covering problem of monotone submodules: select a specified number k of enhanced nodes u1...u k , for each node v, enhance the lower bound of the node's cumulative contribution to v Solving the objective function S2034. Based on the estimated value of S2032, use the random greedy algorithm to solve the lower bound equivalent problem of S2023 to obtain another set of solutions for the enhanced nodes. S2035. Compare the two sets of solutions obtained in S2031 and S2034, estimate the actual benefits of the two sets of solutions as enhanced nodes in the social network by simulating the information propagation process, and take the better set of solutions as the output of the sub-algorithm.

6. The social network influence maximization algorithm with both collaboration and competition under the independent cascade model according to claim 5 is characterized in that: The PR-IMM sub-algorithm and the SA-IMM sub-algorithm can be used to The probability of obtaining an approximate optimal solution with an approximate ratio of 1-1 / e-∈, where e is a natural constant; SA-RG-IMM can The probability of obtaining an approximate optimal solution with an approximate ratio of 1 / e-∈; where |V| is the total number of nodes in the social network graph, Parameters defined by the user.

7. A social network influence maximization system with both collaboration and competition under an independent cascade model, characterized in that: The algorithm for maximizing the influence of a social network with both collaboration and competition under the independent cascade model described in any one of claims 1 to 6 comprises: The designation module is used to designate the priorities of four types of information, Ca+, Ca, Cr and Cr-, according to the input parameters; Ca and Cr represent the positive and negative information spread by the information seed node before passing through the enhancement node, respectively; Ca+ represents the enhanced positive information with greater dissemination ability after passing through the enhancement node; Cr- represents the weakened negative information with less harmfulness after passing through the enhancement node; The determination module is used to determine the sub-algorithm according to the monotonicity and sub-modularity of the four types of information priorities, and the sub-algorithm includes the PR-IMM sub-algorithm, the SA-IMM sub-algorithm and the SA-RG-IMM sub-algorithm.

8. A computer storage medium, characterized in that: The computer storage medium stores a computer program; when the computer program is executed on a computer, the computer executes the social network influence maximization algorithm with both collaboration and competition under the independent cascade model described in any one of claims 1 to 6.

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