A virus propagation control method based on bounded percolation-greedy algorithm

Abstract

The present invention provides a virus propagation control method based on bounded percolation-greedy algorithm. First, extract the target network information to understand the target network nodes and edge attributes; then, based on the percolation theory, continuously occupy specific nodes on the target network to achieve the reverse process of removing key nodes; each time occupy the node that minimizes the objective function, limit the size of the maximum connected component and the degree of the remaining network nodes to control the virus propagation; set the key indicator boundary value, when the key indicators of all candidate nodes exceed the boundary value, update the boundary value to occupy more candidate nodes; finally, use order parameters and network resilience to represent the effect of controlling virus propagation. The present invention can achieve fast and efficient decomposition of large networks, thereby timely controlling virus propagation and reducing the losses caused by it.

Description

Technical Field

[0001] The invention belongs to the technical field of network information analysis, and in particular relates to a virus propagation control method based on a bounded percolation-greedy algorithm. Background Art

[0002] Networks can simulate the interactions within complex systems, where nodes represent individuals in the system and edges represent the interactions between individuals. The application of networks is beneficial to studying the global properties of the system. Networks can test the effects of various artificial measures on real systems and provide optimal solutions for controlling, predicting, optimizing, and reconstructing real systems.

[0003] The network decomposition problem refers to identifying a set of key nodes for a given network, and the removal of this set of key nodes can decompose the network to the greatest extent. Network decomposition can effectively reflect and analyze the actual situation. For example, compared with the diffusion system under the mean field assumption, the network diffusion system can better characterize the virus transmission pattern; by identifying key nodes and decomposing the virus transmission network, the following problems can be solved to a certain extent: 1) When controlling the spread of the virus, which group of people need to be quarantined first? 2) Due to resource constraints and limited number of vaccines, which group of people should be vaccinated first? 3) Which places should be focused on? On the other hand, key nodes dominate the dynamic development of the virus transmission system. Identifying key nodes can help find the source of the spread of the virus and save computing resources.

[0004] The network decomposition problem has been proven to be an NP-hard (Non-deterministic Polynomial-time Hardness) problem. Network decomposition methods are specifically divided into the following four categories: 1) Local information-based methods: This type of method does not require the known network topology structure, and randomly removes nodes from the network to achieve network decomposition, which is usually not efficient enough. Subsequently, the acquaintance algorithm was derived, which achieves network decomposition by randomly selecting a group of nodes and removing one of the neighbor nodes of this group of nodes. Its efficiency is often lower than that of the node centrality-based method. 2) Node centrality-based methods: Node importance is calculated using node indicators such as degree centrality, eigenvector centrality, Pagerank, betweenness centrality, Katz centrality, etc., and nodes with high importance are selected as key nodes. The degree centrality method believes that the higher the degree of the node, the higher the importance. The eigenvector centrality method believes that the nodes connected to the important nodes are also important nodes, so the centrality of the node is obtained by adding the centralities of its neighbors. 3) Heuristic methods: After removing the most important node, the degree of its original neighbor nodes will decrease. Based on the method based on node centrality, the heuristic method recalculates the importance of nodes in the remaining network after each node is removed, and removes the most important nodes again. 4) Indirect method: Indirect method can decompose the network more effectively. The methods based on de-looping include belief propagation guided method, minimum summation and reverse greedy method. By solving the feedback vertex set problem in the de-looping problem, network decomposition can be achieved. The method based on graph partitioning realizes spectral bisection through approximate strategy, and draws vertex separators according to the minimum vertex cover of spectral bisection, but this method directly considers the entire network and is not efficient enough. The FINDER method is based on graph neural network and reinforcement learning to solve the problem of network decomposition. Because it is based on graph neural network, it is theoretically a method that considers local network.

[0005] Applying the above method to achieve network decomposition requires removing many nodes. In actual application scenarios, especially in resource-scarce areas, the resources used to control the spread of the virus are limited. It is impossible to vaccinate too many people, implement quarantine protection, and close too many places, so it is difficult to control the spread of the virus.

[0006] The application efficiency of the above methods is not very high, especially in large networks. For large-scale network data, some methods take too long to calculate or exceed memory limitations, making it difficult to solve the network decomposition problem, such as the GND method based on graph segmentation. In practice, in the face of a large-scale outbreak of virus transmission, it is necessary to take into account real-time information from all parties and respond quickly to prevention and control; however, the above methods are difficult to apply to large networks in practice, and it is difficult to achieve a rapid response to virus transmission. Summary of the invention

[0007] In order to overcome the shortcomings of the prior art, the present invention provides a virus propagation control method based on a bounded percolation-greedy algorithm. First, extract the target network information to understand the target network nodes and edge attributes; then, based on the percolation theory, continuously occupy specific nodes on the target network to achieve the reverse process of removing key nodes; each time the node that minimizes the objective function is occupied, the size of the maximum connected component and the degree of the remaining network nodes are limited to control the spread of the virus; set the critical indicator threshold, and when the critical indicators of all candidate nodes exceed the threshold, update the threshold to occupy more candidate nodes; finally, use order parameters and network resilience to represent the effect of controlling the spread of the virus. The present invention can achieve rapid and efficient decomposition of large networks, thereby timely controlling the spread of the virus and reducing the losses caused by it.

[0008] A virus propagation control method based on bounded percolation-greedy algorithm, characterized by the following steps:

[0009] Step 1: Input the data related to the population involved in virus transmission, including individual information, number of individuals, connections between individuals and the probability of virus transmission. The individuals in the virus transmission population data are taken as nodes, the connections between individuals are edges, and the probability of virus transmission between individuals is the edge weight. The virus transmission network G(N,M) corresponding to the virus transmission population data is constructed. The network point set is N, the edge set is M, and the edge weight between nodes v and w is β vw ;

[0010] Step 2: Initialize all nodes in the virus propagation network to an unoccupied state, forming an unoccupied node set N r (t); Construct candidate node set N c (t), initially the set of unoccupied nodes N r Any subset of (t) whose number of nodes satisfies y≤n, where n is the number of nodes contained in the point set N of the initial network; construct the occupied node set N o (t), initially an empty set; all edges are initialized to an unoccupied state, forming an unoccupied edge set M r (t); Construct the occupied edge set M o (t), initially an empty set; t represents each moment after the virus spread is controlled, initially t = 0, occupying the node sequence S r (t) is an empty sequence; set the critical indicator boundary value Initially 1, temporary value Initially 1;

[0011] Step 3: At time t, select the candidate node set N c(t) is the node that minimizes the objective function ψ(u), and the state of the node is converted to the occupied state. If there are multiple nodes that minimize the objective function ψ(u) at the same time, one of the nodes is randomly selected and converted to the occupied state; then, the node is added to the set of unoccupied nodes N r (t), candidate node set N c (t) is deleted and added to the occupied node set N o (t) and added to the occupied node sequence S r (t); if two adjacent nodes are both occupied, the edge between the two nodes is converted to an occupied state, and the edge is added to the unoccupied edge set M r (t) is deleted and added to the occupied edge set M o (t) medium;

[0012] Step 4: At time t, the candidate node set N c The key index I of all nodes in (t) exceeds the key index threshold When t=t+1, go to step 5; otherwise, t=t+1, return to step 3;

[0013] Step 5: If the key indicator thresholds have been updated since the last time At the current time t, at least one node in the network has been selected to be in the occupied state, then the critical indicator boundary value is set to Update to α×minI, and then temporarily store the value Update to new Otherwise, the key indicator threshold Updated to Re-store value Update to new

[0014] After the update is completed, determine whether t is greater than the number of nodes n. If so, use the occupied node sequence S obtained at this time r (t) is the final occupied node sequence, go to step 6, otherwise, t = t + 1, return to step 3; the α is the update parameter, α>1;

[0015] Step 6: Convert all nodes to unoccupied state again, according to the occupied node sequence S r (t) The internal order transforms the nodes into occupied states one by one; each time a node state transformation is performed, the order parameter G is calculated. a (q); When the order parameter increases from 0 to a non-zero constant for the first time, the unoccupied node ratio q at this time is recorded as the unoccupied node ratio threshold q c , unoccupied node ratio threshold q c Represents the minimum node ratio that needs to be removed to control the spread of the virus. The smaller its value, the smaller the node ratio that needs to be removed to control the spread of the virus.r When all nodes in (t) are transformed into occupied state, the network resilience F is calculated. The network resilience F represents the virus propagation control effect. The smaller its value is, the better the virus propagation control effect is.

[0016] Specifically, the unoccupied node set N described in step 2 r (t) and the set of occupied nodes N o (t), at any time, the intersection is empty, the union is the point set N; the unoccupied edge set M r (t) and the occupied edge set M o (t), at any time the intersection is empty and the union is the edge set M.

[0017] Specifically, the objective function ψ(u) described in step 3 is set as:

[0018]

[0019] Among them, for the candidate node set N c For node u in (t), ψ(u) represents the objective function value, and I(u) represents the key indicator value of node u; is a function about node u, for any The node u, Set to an equal finite value.

[0020] Specifically, the key indicator I described in step 4 is set to the external degree of the node, and the calculation formula is:

[0021]

[0022] in, represents the external degree of node u, c(u) is the connected component where node u is located after it turns to occupied state, v represents the node in the connected component c(u); k v is the degree of node v in the initial network G(N,M), k v ' is the node v in the occupied network G(N o (t),M o (t)) in the degree, the occupied network G(N o (t),M o (t)) refers to the set of nodes N occupied at time t o The set of nodes and occupied edges in (t) o The edges in (t) are connected to form a network according to the structure of the initial network G(N,M); the connected components are sub-networks of the virus propagation network; and the node degree is the number of edges connected to the node.

[0023] Specifically, the key indicator I described in step 4 is set to the external propagation probability of the node, and the calculation formula is:

[0024]

[0025] in, represents the external propagation probability of node u, c(u) is the connected component where node u is located after it turns to the occupied state, v represents the nodes in the connected component c(u); Γ(v) represents the set of unoccupied neighbor nodes of node v; w represents the nodes in the set Γ(v); β vw represents the edge weight between nodes v and w.

[0026] Specifically, the occupied node sequence S obtained in step 6 is r The internal order of (t) refers to the optimal occupied node order for the virus spread to change from being controlled to being uncontrolled.

[0027] Specifically, the order parameter G described in step 6 a The calculation formula of (q) is:

[0028]

[0029] Where q is the proportion of unoccupied nodes in the network, c" max is the maximum connected component, |c” max | is the number of nodes contained in the maximum connected component, and the maximum connected component is the sub-network containing the largest number of nodes when the proportion of unoccupied nodes in the network is q.

[0030] Specifically, the calculation formula of the network resilience F described in step 6 is:

[0031]

[0032] The beneficial effects of the present invention are as follows: due to the adoption of a percolation process of continuously occupying nodes and a specific objective function design strategy, the present invention can be used to solve the problem of rapid decomposition of large networks, and has a higher network decomposition efficiency, thereby timely and effectively controlling virus propagation and reducing the losses caused by it; the present invention realizes network decomposition, removes fewer nodes, and has a smaller scale of virus propagation, so that fewer resources are consumed in controlling virus propagation. When resources are scarce, the present invention is used to control virus propagation, which can theoretically provide better protection for the network and achieve the purpose of saving protection costs; the present invention has lower time complexity and space complexity, higher computational efficiency, and can quickly respond to sudden virus propagation events; it performs better for large-scale network data and is suitable for network decomposition problems in large networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1It is a flow chart of the virus propagation control method based on bounded percolation-greedy algorithm of the present invention;

[0034] Figure 2 It is a schematic diagram of the node external degree of the present invention;

[0035] Figure 3 It is a schematic diagram of the results of the change of the order parameter with respect to the proportion of unoccupied nodes obtained by using different methods in four different networks; in the figure, (a) - a schematic diagram of the results of the change of the order parameter with respect to the proportion of unoccupied nodes obtained by using different methods in the Power network, (b) - a schematic diagram of the results of the change of the order parameter with respect to the proportion of unoccupied nodes obtained by using different methods in the loc-Gowalla network, (c) - a schematic diagram of the results of the change of the order parameter with respect to the proportion of unoccupied nodes obtained by using different methods in the twitter-L network, (d) - a schematic diagram of the results of the change of the order parameter with respect to the proportion of unoccupied nodes obtained by using different methods in the as-Skitter network;

[0036] Figure 4 It is a schematic diagram of the computation time of different methods in different networks. DETAILED DESCRIPTION

[0037] The present invention is further described below in conjunction with the accompanying drawings and embodiments. The present invention includes but is not limited to the following embodiments.

[0038] like Figure 1 As shown, the present invention provides a virus propagation control method based on bounded percolation-greedy algorithm, and its specific implementation process is as follows:

[0039] Step 1: Input the data related to the population involved in virus transmission, including individual information, number of individuals, connections between individuals and the probability of virus transmission. The individuals in the virus transmission population data are taken as nodes, the connections between individuals are edges, and the probability of virus transmission between individuals is the edge weight. The virus transmission network G(N,M) corresponding to the virus transmission population data is constructed. The network point set is N, the edge set is M, and the edge weight between nodes v and w is β vw .

[0040] Step 2: Initialize all nodes in the virus propagation network to an unoccupied state, forming an unoccupied node set N r (t); Construct candidate node set N c (t), initially the set of unoccupied nodes N r Any subset of (t) whose number of nodes satisfies y≤n, where n is the number of nodes contained in the point set N of the initial network; construct the occupied node set N o (t), initially an empty set; all edges are initialized to an unoccupied state, forming an unoccupied edge set M r(t); Construct the occupied edge set M o (t), initially an empty set. The set of unoccupied nodes N r (t) and the set of occupied nodes N o (t), at any time, the intersection is empty, the union is the point set N; the unoccupied edge set M r (t) and the occupied edge set M o (t), at any time the intersection is empty and the union is the edge set M.

[0041] t represents each moment after the virus spread is controlled. Initially, t = 0, occupying the node sequence S r (t) is an empty sequence; set the critical indicator boundary value Initially 1, temporary value Initially 1.

[0042] Step 3: At time t, select the candidate node set N c (t) is the node that minimizes the objective function ψ(u), and the state of the node is converted to the occupied state. If there are multiple nodes that minimize the objective function ψ(u) at the same time, one of the nodes is randomly selected and converted to the occupied state; then, the node is added to the set of unoccupied nodes N r (t), candidate node set N c (t) is deleted and added to the occupied node set N o (t) and added to the occupied node sequence S r (t); if two adjacent nodes are both occupied, the edge between the two nodes is converted to an occupied state, and the edge is added to the unoccupied edge set M r (t) is deleted and added to the occupied edge set M o (t) in.

[0043] Among them, the objective function ψ(u) is set as:

[0044]

[0045] Among them, for the candidate node set N c For node u in (t), ψ(u) represents the objective function value, and I(u) represents the key indicator value of node u; is a function about node u, for any The node u, Set to an equal finite value.

[0046] Step 4: At time t, the candidate node set N c The key index I of all nodes in (t) exceeds the key index threshold When t=t+1, go to step 5; otherwise, t=t+1, return to step 3.

[0047] Among them, the key indicator I can be set in two ways:

[0048] (1) The key indicator I is set to the external degree of the node, and the calculation formula is:

[0049]

[0050] in, represents the external degree of node u, c(u) is the connected component where node u is located after it turns to occupied state, v represents the node in the connected component c(u); k v is the degree of node v in the initial network G(N,M), k v ' is the node v in the occupied network G(N o (t),M o (t)) in the degree, the occupied network G(N o (t),M o (t)) refers to the set of nodes N occupied at time t o The set of nodes and occupied edges in (t) o The edges in (t) are connected to form a network according to the structure of the initial network G(N,M); the connected components are subnetworks of the virus transmission network; the node degree is the number of edges connected to the node. Figure 2 As shown in the figure, black solid nodes represent occupied nodes, gray solid nodes and hollow nodes represent unoccupied nodes, solid lines represent occupied edges, dotted lines represent unoccupied edges, and light gray block-shaped covered parts represent connected components. For example, nodes u, j, and w are unoccupied nodes, and nodes v and i are unoccupied nodes; if the unoccupied node u is converted to an occupied state, the connected component c(u) where node u is located contains nodes u and v. The external degree of node u is calculated according to the formula: Similarly, if the unoccupied node j is converted to an occupied state, the connected component of node j is c(j), and the external degree of node j is

[0051] (2) The key indicator I is set as the external propagation probability of the node, and the calculation formula is:

[0052]

[0053] in, represents the external propagation probability of node u, c(u) is the connected component where node u is located after it turns to the occupied state, v represents the nodes in the connected component c(u); Γ(v) represents the set of unoccupied neighbor nodes of node v; w represents the nodes in the set Γ(v); β vw represents the edge weight between nodes v and w.

[0054] Step 5: If the key indicator thresholds have been updated since the last time At the current time t, at least one node in the network has been selected to be in the occupied state, then the critical indicator boundary value is set to Update to α×minI, and then temporarily store the value Update to new Otherwise, the key indicator threshold Updated to Re-store value Update to new

[0055] After the update is completed, determine whether t is greater than the number of nodes n. If so, use the occupied node sequence S obtained at this time r (t) is the final occupied node sequence, go to step 6, otherwise, t = t + 1, return to step 3; the α is the update parameter, α>1;

[0056] Step 6: Convert all nodes to unoccupied state again, according to the occupied node sequence S r (t) The internal order transforms the nodes into occupied states one by one. The occupied node sequence S r The internal order of (t) refers to the optimal occupied node order for the virus spread to change from being controlled to being uncontrolled.

[0057] Each time a node state transformation is performed, the order parameter G is calculated. a (q), order parameter G a (q) represents the degree to which the virus propagation in the current network changes from being controlled to being uncontrolled. The smaller the order parameter, the greater the degree to which the virus propagation in the current network is controlled. a The calculation formula of (q) is:

[0058]

[0059] Where q is the proportion of unoccupied nodes in the network, c" max is the maximum connected component, |c” max | is the number of nodes contained in the maximum connected component. The maximum connected component is the sub-network containing the largest number of nodes when the proportion of unoccupied nodes in the network is q, representing the scale of the infected population spread by the virus.

[0060] The process of continuously converting nodes to occupied states in the network can be seen as a reverse percolation process of continuously removing nodes from the complete network. The node selection order of the two is inverted, and the application effect is reversed. The unoccupied state of a node or edge is the same as the removed state. Nodes come into contact with each other through edges and spread the virus. If some nodes and their edges are removed and the current network is decomposed into multiple blocks, the contact between nodes in the occupied state and other nodes can be blocked, limiting the widespread spread of the virus. Therefore, the proportion of unoccupied nodes q, or the proportion of removed nodes, represents the size of the population that is immune or isolated during virus transmission, reflecting the strength of prevention and control measures.

[0061] When this step starts to transform the node state, the unoccupied node ratio q is 1 and the order parameter is 0. As the number of occupied nodes increases, the unoccupied node ratio q gradually decreases and the order parameter gradually increases. When the order parameter increases from 0 to a non-zero constant for the first time, the maximum connected component appears and the virus begins to spread widely. The unoccupied node ratio q at this time is recorded as the unoccupied node ratio threshold q c , unoccupied node ratio threshold q c represents the minimum node ratio required to be removed to control the spread of the virus, q c The smaller it is, the smaller the number of nodes that need to be removed to control the spread of the virus, and the smaller the population that needs to be immunized or isolated.

[0062] When occupying node sequence S r When all nodes in (t) are transformed into occupied state, the network resilience F is calculated. The network resilience F represents the virus propagation control effect. The smaller its value is, the better the virus propagation control effect is.

[0063] The calculation formula of network resilience F is:

[0064]

[0065] In order to verify the effectiveness of the method of the present invention, an experiment was conducted on a virus propagation network, and its network parameters are shown in Table 1.

[0066] Table 1

[0067] Dataset Number of nodes Number of edges Yeast 2375 11693 Power 4941 6594 p2p-Gnutella08 6301 20777 CA-AstroPh 18771 198050 Email-Enron 36692 183831 loc-Gowalla 196591 950327 twitter-L 532325 694606 web-Google 875713 4322051 PAroad 1088092 1541898 Flickr 1624991 15473043 as-Skitter 1696415 11095298 LiveJournal 3997962 34681189

[0068] Five commonly used network decomposition methods, HD (Higher Degree, degree centrality) method, AHD (Adaptive Higher Degree, adaptive degree centrality) method, AMSRGS (Min-sum and Reverse-greedyStrategy, minimum sum and reverse greedy strategy) method, GND (Generalized network dismantling, generalized network decomposition) method, FINDER (FInding key players in Networks through DEepReinforcement learning, deep reinforcement learning to find key nodes) method, and the method of the present invention BPG-I (Bounded-Percolation Greedy-I, a bounded percolation-greedy method with the key indicator being the external degree) and BPG-II (Bounded-Percolation Greedy-II, a bounded percolation-greedy method with the key indicator being the external propagation probability) are selected for comparative experiments. Table 2 shows the network resilience F values ​​obtained by using different methods on different networks, and Table 3 shows the unoccupied node ratio threshold q obtained by using different methods on different networks c .

[0069] Table 2

[0070]

[0071]

[0072] Table 3

[0073]

[0074] It can be seen from Table 2 that compared with the HD, AHD, and FINDER methods, the network resilience F of the BPG-I method is reduced by more than 30%; compared with the AMSRGS and GND methods, the network resilience F of the BPG-I method is reduced by more than 20%; compared with the BPG-II method, the network resilience F of the BPG-I method is increased by about 5%; it can be seen that compared with other methods, the BPG-I and BPG-II methods of the present invention have better virus propagation control effects, and the control effect of the BPG-II method is slightly better than that of BPG-I.

[0075] It can be seen from Table 3 that compared with the HD, AHD, GND, and FINDER methods, the unoccupied node ratio threshold q of the BPG-I method is c Compared with the AMSRGS method and the BPG-II method, the unoccupied node ratio threshold q of the BPG-I method is cThe overall values ​​are similar. On the PAroad and as-Skitter networks, the unoccupied node ratio threshold q of the BPG-I method is c Compared with the AMSRGS method, it is reduced by more than 10%. Compared with other methods, the BPG-I and BPG-II methods of the present invention require a smaller proportion of nodes to be removed to control virus transmission, and the size of the population that needs to be immunized or isolated is smaller;

[0076] In Table 2 and Table 3, “-” means that the calculation time is too long or exceeds the memory limit. For large-scale networks such as Flickr and LiveJournal, the GND method is difficult to achieve network decomposition due to the limitation of calculation time and space. In the LiveJournal network, the AMSRGS and FINDER methods have the same problem. The BPG-I and BPG-II methods of the present invention can achieve network decomposition in large-scale networks such as Flickr and LiveJournal, and compared with the HD and AHD methods, the network resilience F is reduced by more than 10%, and the unoccupied node ratio threshold q is c It is reduced by more than 20%. It can be seen that the present invention performs well on large-scale networks.

[0077] Figure 3 The results of the order parameter changes on the Power, loc-Gowalla, twitter-L, and as-Skitter networks obtained by different methods with respect to the proportion of removed nodes are given. In the figure, the horizontal axis q is the proportion of unoccupied nodes in the network, and the vertical axis G is a (q) is the order parameter; HD is the degree centrality method, AHD is the adaptive degree centrality method, FINDER is the deep reinforcement learning method for finding key nodes, BPG-I is the method of the present invention using the node external degree as the key indicator, and BPG-II is the method of the present invention using the external propagation probability as the key indicator.

[0078] Under the condition that the ratio q of removed nodes is constant, the order parameter G obtained by the present invention is a (q) is often smaller, and the degree to which the virus spread is controlled is often greater. For example, in the Power network, when the ratio of removed nodes q is 0.03, the BPG-I method obtains the order parameter G a (q) is 0.0820, and the order parameter G is obtained by the FINDER method. a (q) is 0.7758; it can be seen that, corresponding to the actual situation, under the condition of immunizing or isolating the same proportion of patients, the scale of the infected population caused by the virus transmission of the present invention is smaller, and the degree of virus transmission is more controlled;

[0079] After obtaining the order parameter G a(q) is constant, the ratio q of removed nodes in the method of the present invention is smaller; for example, in the loc-Gowalla network, when G a When (q) is 0.01, the removed node ratio q of the BPG-I method is 0.1354, and the removed node ratio q of the FINDER method is 0.1919; it can be seen that, corresponding to the actual situation, under the condition that the degree of virus transmission is controlled to the same extent, the proportion of patients immunized or isolated using the present invention is smaller.

[0080] Figure 4 A comparison chart of the computing time of different methods on different networks is given. In the chart, the horizontal axis represents different networks, namely Yeast, Power, p2p (p2p-Gnutella08), CA (CA-AstroPh), Email (Email-Enron), loc (loc-Gowalla), twitter (twitter-L), web (web-Google), PAroad, Flickr, as (as-Skitter), and Live (LiveJournal). The vertical axis Time represents the computing time. In the legend, AMSRGS is the minimum sum and reverse greedy method.

[0081] Compared with the AMSRGS and FINDER methods, the calculation time of the BPG-I and BPG-II methods of the present invention is significantly reduced and the efficiency is significantly improved; for example, in the as-Skitter network, the calculation speed of the BPG-I method is increased by more than 1500 times compared with the AMSRGS method, and by more than 70 times compared with the FINDER method; it can be seen that the present invention has high calculation efficiency and can quickly respond to sudden virus transmission events.

[0082] In summary, the method of the present invention achieves network decomposition, removes fewer nodes, and has a smaller scale of virus propagation. The method of the present invention is used to control virus propagation when resources are scarce, which can theoretically provide better protection for the network. The method of the present invention has lower time complexity and space complexity, higher computational efficiency, better performance for large-scale network data, and is suitable for network decomposition problems in large networks.

Claims

1. A virus propagation control method based on bounded percolation-greedy algorithm, characterized in that Here are the steps: Step 1: Input the data related to the population involved in virus transmission, including individual information, number of individuals, connections between individuals and the probability of virus transmission. The individuals in the virus transmission population data are taken as nodes, the connections between individuals are edges, and the probability of virus transmission between individuals is the edge weight. The virus transmission network G(N,M) corresponding to the virus transmission population data is constructed. The network point set is N, the edge set is M, and the edge weight between nodes v and w is β vw ; Step 2: Initialize all nodes in the virus propagation network to an unoccupied state, forming an unoccupied node set N r (t); Construct candidate node set N c (t), initially the set of unoccupied nodes N r Any subset of (t) whose number of nodes satisfies y≤n, where n is the number of nodes contained in the point set N of the initial network; construct the occupied node set N o (t), initially an empty set; all edges are initialized to an unoccupied state, forming an unoccupied edge set M r (t); Construct the occupied edge set M o (t), initially an empty set; t represents each moment after the virus spread is controlled, initially t = 0, occupying the node sequence S r (t) is an empty sequence; set the critical indicator boundary value Initially 1, temporary value Initially 1; Step 3: At time t, select the candidate node set N c (t) is the node that minimizes the objective function ψ(u), and the state of the node is converted to the occupied state. If there are multiple nodes that minimize the objective function ψ(u) at the same time, one of the nodes is randomly selected and converted to the occupied state; then, the node is added to the set of unoccupied nodes N r (t), candidate node set N c (t) is deleted and added to the occupied node set N o (t) and added to the occupied node sequence S r (t); if two adjacent nodes are both occupied, the edge between the two nodes is converted to an occupied state, and the edge is added to the unoccupied edge set M. r (t) is deleted and added to the occupied edge set M o (t) medium; Step 4: At time t, the candidate node set N c The key index I of all nodes in (t) exceeds the key index threshold When t=t+1, go to step 5; otherwise, t=t+1, return to step 3; Step 5: If the key indicator thresholds have been updated since the last time At the current time t, at least one node in the network has been selected to be in the occupied state, then the critical indicator boundary value is set to Update to α×minI, and then temporarily store the value Update to new Otherwise, the key indicator threshold Updated to Re-store value Update to new After the update is completed, determine whether t is greater than the number of nodes n. If so, use the occupied node sequence S obtained at this time r (t) is the final occupied node sequence, go to step 6, otherwise, t = t + 1, return to step 3; the α is the update parameter, α>1; Step 6: Convert all nodes to unoccupied state again, according to the occupied node sequence S r (t) The internal order transforms the nodes into occupied states one by one; each time a node state transformation is performed, the order parameter G is calculated. a (q); When the order parameter increases from 0 to a non-zero constant for the first time, the unoccupied node ratio q at this time is recorded as the unoccupied node ratio threshold q c , unoccupied node ratio threshold q c Represents the minimum node ratio that needs to be removed to control the spread of the virus. The smaller its value, the smaller the node ratio that needs to be removed to control the spread of the virus. r When all nodes in (t) are transformed into occupied state, the network resilience F is calculated. The network resilience F represents the virus propagation control effect. The smaller its value is, the better the virus propagation control effect is.

2. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The set of unoccupied nodes N described in step 2 r (t) and the set of occupied nodes N o (t), at any time, the intersection is empty, the union is the point set N; the unoccupied edge set M r (t) and the occupied edge set M o (t), at any time the intersection is empty and the union is the edge set M.

3. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The objective function ψ(u) described in step 3 is set as: Among them, for the candidate node set N c For node u in (t), ψ(u) represents the objective function value, and I(u) represents the key indicator value of node u; is a function about node u, for any The node u, Set to an equal finite value.

4. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The key indicator I described in step 4 is set to the external degree of the node, calculated as: in, represents the external degree of node u, c(u) is the connected component where node u is located after it turns to occupied state, v represents the node in the connected component c(u); k v is the degree of node v in the initial network G(N,M), k′ v is the node v in the occupied network G(N o (t),M o (t)) in the degree, the occupied network G(N o (t),M o (t)) refers to the set of nodes N occupied at time t o The set of nodes and occupied edges in (t) o The edges in (t) are connected to form a network according to the structure of the initial network G(N,M); the connected components are sub-networks of the virus propagation network; and the node degree is the number of edges connected to the node.

5. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The key indicator I described in step 4 is set to the external propagation probability of the node, which is calculated as: in, represents the external propagation probability of node u, c(u) is the connected component where node u is located after it turns to the occupied state, v represents the nodes in the connected component c(u); Γ(v) represents the set of unoccupied neighbor nodes of node v; w represents the nodes in the set Γ(v); β vw represents the edge weight between nodes v and w.

6. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The occupied node sequence S is obtained in step 6 r The internal order of (t) refers to the optimal occupied node order for the virus spread to change from being controlled to being uncontrolled.

7. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The order parameter G described in step 6 a The calculation formula of (q) is: Where q is the proportion of unoccupied nodes in the network, c″ max is the maximum connected component, |c″ max | is the number of nodes contained in the maximum connected component, and the maximum connected component is the sub-network containing the largest number of nodes when the proportion of unoccupied nodes in the network is q.

8. The virus propagation control method based on bounded percolation-greedy algorithm as claimed in claim 1, characterized in that: The calculation formula for network resilience F described in step 6 is: 。

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