CN107800797A - A kind of distributed game centrad method for solving - Google Patents

Abstract

The invention discloses a method for solving distributed game centrality, belonging to the field of parallel and distributed computing, comprising: according to the definition of traditional centrality, dividing the graph into a set of elements θ; according to each node in the graph, distributed Find the contribution information of each node to each element, according to the contribution information of each node to each element, collect the contribution information of all nodes to each element in the set in a distributed manner, and calculate the distribution for each element θ, a The contribution information of the set C of nodes with size k to the element θ is broadcast in the graph. The contribution information of C to the element θ; according to the contribution information of each node to each element and the contribution information of each node distributed computing community , get the change of each node’s contribution to the group, and then get the game centrality of each node. The invention greatly reduces the time complexity of the centralized solution to the centrality of the game, and can process large-scale graph data more quickly.

Description

A Method for Solving the Centrality of Distributed Game

technical field

The invention belongs to the field of parallel and distributed computing, and more specifically relates to a method for solving distributed game centrality.

Background technique

Given a point or an edge in the network, determining whether it is more important (more central) than other nodes or edges in the network has become a key research topic, and it is in the fields of social network analysis, biology, computer science, etc. have received widespread attention. To this end, researchers have proposed a series of traditional centrality to measure the importance of a point or an edge. At present, there are mainly degree centrality, betweenness centrality, closeness centrality and eigenvalue centrality. So far, centralized solutions to traditional centralities have been extensively studied, and most of the traditional centralities can be solved in polynomial time.

Recently, the idea of cooperative game theory, such as Shapley value, Banzhaf index, and more general Semivalue, has been introduced into the calculation of traditional centrality, and the calculation method of expanding traditional centrality has attracted widespread attention. The main idea of game-based network centrality is to regard the nodes in the network as participants in a cooperative game, where a cooperative game is a game played by some participants in an alliance and cooperative manner. In this combination, the contribution segmentation idea in the game theory solution is introduced into the network analysis. Now this method has been widely used, for example, in social and organizational network analysis, in biological network analysis, and covert network analysis. Since the group size is arbitrary, the number of all groups reaches an exponential level, resulting in an exponential time complexity for solving the game centrality, which is unacceptable in a centralized solution.

Researchers have proposed an effective method for solving centrality based on game theory in a centralized manner. Among them, degree centrality, betweenness centrality and close centrality based on Shapley value and Semivalue can all be solved in polynomial time . However, there are many other centrality methods that have not been extended to game-theoretic centrality. In response to this problem, researchers have recently proposed a framework, so that for a centrality based on cooperative games, no matter which game theory it is based on or which centrality it is, as long as certain conditions are met, it can be Solve in polynomial time.

Although researchers have proposed a computing framework in polynomial time for the solution method based on game centrality, for large-scale graphs, the time-consuming of this method is too high, making it unacceptable to run on a single machine.

Contents of the invention

Aiming at the above defects or improvement needs of the prior art, the present invention provides a distributed game centrality solution method, the purpose of which is to give a given arbitrary game centrality, according to distributed computing rules and characteristics, in distributed Solve the game centrality of each node in the environment. The method of the invention solves the problem that the centralized algorithm takes too long to solve the problem, and can solve the game centrality more quickly.

In order to achieve the above object, the present invention provides a method for solving distributed game centrality, including:

S1, according to the definition of traditional centrality, divide the graph into a set of elements θ;

S2, according to each node in the graph, distribute the contribution information of each node to each element, and the contribution information includes positive contribution, negative contribution and no contribution;

S3, according to the contribution information of each node to each element, the contribution information of all nodes to each element in the set is distributed, and the node set P ^-1 (θ) with positive contribution to the element is obtained, and the negative contribution to the element is obtained The node set R ^-1 (θ) of the node set N ^-1 (θ) that does not contribute to the element;

S4, according to the node sets P ^-1 (θ), R ^-1 (θ) and N ^-1 (θ), distributedly calculate the contribution information of a node set C with a size of k to the element θ for each element θ , broadcast the contribution information of C to element θ in the graph, so that each node in the graph knows the contribution information of other nodes to all elements;

S5, according to the contribution information of each node to each element and the contribution information to each node's distributed computing community, the community is a set of k nodes selected from other nodes, and the contribution change of each node to the community is obtained, and then Get the game centrality of each node.

Further, the traditional centrality is degree centrality, betweenness centrality or closeness centrality.

Further, the traditional centrality is degree centrality or close centrality, and the specific implementation of step S1 is: according to the definition of degree centrality or close centrality, the graph is divided into a collection of nodes, and each node is regarded as is an element θ.

Further, the traditional centrality is betweenness centrality, and the specific implementation of the step S1 is: according to the definition of betweenness centrality, the graph is divided into a set of elements θ, and each element is a node pair.

Further, step S3 includes:

S3.1, according to the contribution information of each node to each element, a breadth-first search tree is distributed in the graph;

S3.2, randomly select a node from the graph as the root node of the breadth-first search tree, and the root node distributedly collects the contribution information of each node to each element; obtain the node set P ^-1 ( θ), the node set R ^-1 (θ) that has a negative contribution to the element, and the node set N ^-1 (θ) that does not contribute to the element.

Further, the contribution of each node to the community changes as follows:

When the node i contributes positively to the element θ, but the group makes no contribution to the element θ, then the contribution of the node to the group becomes a positive contribution;

When node i makes a negative contribution to the element θ, and the group contributes positively to the element θ, the contribution of the node to the group changes as a negative contribution;

When node i makes a positive contribution or no contribution to the element θ, and the group makes a positive contribution to the element θ, the contribution of the node to the group changes to no contribution.

Further, the game centrality is:

Among them, ν is the definition of traditional centrality, is the game centrality of node i, k represents the number of nodes, β(k) represents a function related to the size of k, C _k represents a group of size k, represents the expectation of C _k , MC(C _k , i) represents the contribution change of node i to group C _k , and V represents the set of nodes in the graph.

Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

(1) The present invention proposes to solve the game centrality in a distributed environment for the first time; for a given arbitrary game centrality, according to the distributed computing rules and characteristics, the game centrality of each node is solved in a distributed environment. The invention solves the problem that the centralized algorithm takes too long to solve the problem, and the invention can solve the game centrality more quickly.

(2) The distributed method for solving the game centrality provided by the present invention greatly reduces the time complexity of the centralized solution for the game centrality, and can process large-scale graph data faster. The distributed computing designed by the present invention can effectively avoid congestion caused by too many messages sent by nodes.

Description of drawings

Fig. 1 is the flow chart of a kind of distributed game centrality solution method provided by the embodiment of the present invention;

Fig. 2 is the graph data structure provided by Embodiment 1 of the present invention;

Fig. 3 is a flow chart of collecting contribution information provided by Embodiment 1 of the present invention;

Fig. 4 is the flowchart of constructing a breadth-first search tree provided by Embodiment 1 of the present invention;

FIG. 5 is a flow chart of distributed collection of contribution information of each node to each element by the root node provided by Embodiment 1 of the present invention;

FIG. 6 is a flow chart of obtaining contribution information of C to element θ provided by Embodiment 1 of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not constitute a conflict with each other.

As shown in Figure 1, the present invention provides a method for solving distributed game centrality, including:

S1, according to the definition of traditional centrality, divide the graph into a set of elements θ; traditional centrality is degree centrality, betweenness centrality or closeness centrality. The traditional centrality is degree centrality or close centrality. According to the definition of degree centrality or close centrality, the graph is divided into a collection of nodes, and each node is regarded as an element θ. The traditional centrality is betweenness centrality. According to the definition of betweenness centrality, the graph is divided into a set of elements θ, and each element is a node pair.

S2, according to each node in the graph, distribute the contribution information of each node to each element, and the contribution information includes positive contribution, negative contribution and no contribution;

S3, according to the contribution information of each node to each element, a breadth-first search tree is distributed in the graph; a node is randomly selected from the graph as the root node of the breadth-first search tree, and the root node distributes and collects each Contribution information of nodes to each element; get the node set P ^-1 (θ) that contributes positively to the element, the node set R ^-1 (θ) that contributes negatively to the element, and the node set N ^- that does not contribute to the element ¹ (θ).

S4, according to the node sets P ^-1 (θ), R ^-1 (θ) and N ^-1 (θ), distributedly calculate the contribution information of a node set C with a size of k to the element θ for each element θ , broadcast the contribution information of C to element θ in the graph, so that each node in the graph knows the contribution information of other nodes to all elements;

S5, according to the contribution information of each node to each element and the contribution information of each node to the distributed computing community, the community is a set of k nodes selected from other nodes, and the contribution of each node to the community is obtained. The change of the contribution of a node to the group is: when the node i makes a positive contribution to the element θ, but the group makes no contribution to the element θ, then the contribution of the node to the group changes as a positive contribution; when the node i makes a negative contribution to the element θ, and If the group contributes positively to the element θ, the change of the node’s contribution to the group is a negative contribution; when the node i makes a positive contribution or no contribution to the element θ, and the group makes a positive contribution to the element θ, then the change of the node’s contribution to the group is no contribute. Then get the game centrality of each node.

Among them, ν is the definition of traditional centrality, is the game centrality of node i, k represents the number of nodes, β(k) represents a function related to the size of k, C _k represents a group of size k, represents the expectation of C _k , MC(C _k , i) represents the contribution change of node i to group C _k , and V represents the set of nodes in the graph.

Example 1

The method for solving game centrality distributedly of the present invention comprises the following steps:

S1, according to the given definition of traditional centrality ν, define the game centrality of node i Among them, k represents the number of nodes, β(k) represents a function related to the size of k, C _k represents a group of size k, represents the expectation of C _k , MC(C _k , i) represents the edge contribution of node i to community C _k ie MC(C _k , i)=ν(C _k ∪i)-ν(C _k ). According to the traditional definition of centrality, the graph G is divided into a set of h(G) elements θ (such as all paths or all shortest paths, where the elements are each path or each shortest path). In this example, we choose degree centrality as the traditional centrality ν. The degree centrality of a set C refers to the sum of the number of nodes connected to the nodes in this set and not in the set C. Take Figure 2 as an example, assuming C={a}, since the number of nodes connected to point a is 2, so v(C)=2, assuming C={a, b, c}, since it is related to all nodes in the set The connected points are {a, b, c, d}, and {a, b, c} are in the set, so v(C)=1. According to the definition of traditional centrality, the graph is divided into a collection of nodes, and each node is regarded as an element.

S2. For each node v, calculate its contribution to each element in a distributed manner. If node v contributes positively to element θ, we will record it as P(v, θ). If node v is negative to element θ contribution, it is recorded as R(v, θ), and if node v has no contribution to element θ, it is recorded as N(v, θ). In the embodiment, taking point a as an example, if the element we select is a, since these two points are the same point, a has a negative contribution to a, and we get R(a, a). If we take neighbors b or d of a as specific elements, since b and d are neighbors of a, we get P(a,b) and P(a,d). If we pick c as a specific element, since c is not directly adjacent to a, c has no effect on a, we get N(a,c).

S3, for each element θ, collect the information contributed by all nodes in a distributed manner. The set of nodes with positive contributions to it is marked as P ^-1 (θ), the set of negative contributions is marked as R ^-1 (θ), and the set of non-contributing nodes is marked as N ^-1 (θ);

As shown in Figure 3, step S3 includes the following sub-steps:

S3.1, according to the contribution of each node to h(G) elements in step S2, given a specific element, the contribution of all points in the graph to this element can be collected.

S3.2, build a breadth-first search tree distributedly in the graph. As shown in Figure 4, this step includes the following sub-steps:

S3.2.1, randomly select a node as the root node. In Figure 2, without loss of generality, select a as the root node.

S3.2.2, the root node sends a message to its neighbor nodes. In Figure 2, a sends a message to its neighbors b, d.

S3.2.3, if the node that received the message has not received the message before, randomly select a node that sent the message to it as its parent node, then the node is the child node of the parent node, and the node sends to its neighbors information. Since neither b nor d has received any messages, and only a sends messages to b and d, both b and d regard a as their parent node. At the same time, point b sends messages to its neighbors a and c, and point d also sends messages to its neighbors Its neighbors b and c send messages.

S3.2.4, repeat step S3.2.3 until every node in the graph has received the message. When c receives a message from b and d, since c has not received a message before, c randomly selects one of points b and d as its parent node, without loss of generality, c selects point b as its parent node . At the same time c sends a message to its neighbors b and d. Since both b and d have received the message before, all nodes in the figure have received the message so far, and step S3.2.4 ends.

S3.3, the root node of the tree collects the contribution of each point to the element. As shown in Figure 5, the sub-steps of this step are as follows:

S3.3.1, each node v is initialized as a queue about the element θ (one of P(v, θ), N(v, θ) or R(v, θ)), and initially the queue only saves its Contribution to element θ. For example, the initialization queue of point a is {R(a, a)}, the initialization queue of point b is {P(b, a)}, the initialization queue of point c is {N(c, a)}, and the initialization queue of point d The queue is {P(d, a)}.

S3.3.2, each node selects an unsent message from the queue and passes it to its parent node. In Figure 1, without loss of generality, assuming that the elements of point a are to be collected, then c will pass N(c, a) to its parent node b, and d will pass P(d, a) to its parent node a , b passes P(b, a) to its parent node a. Since point a is the root node, a will not continue to propagate after receiving the message.

S3.3.3, after each node receives the message, it puts it into the queue it saves. Then when b receives N(c, a), it puts N(c, a) into the queue where it holds the elements of a.

S3.3.4, repeat S3.3.2 until no node in the graph needs to send a message. Since there are unsent messages N(c, a) in b, b will also send N(c, a) to the parent node a.

S3.4, the root node broadcasts all the messages it receives, so that all nodes know the contribution of other nodes to the element. Point a broadcasts all element messages it receives, since point a knows R(a, a), P(b, a), P(d, a), and N(c, a), it sends these information Give its child nodes b, d. When d and b receive the message, since d has no child nodes, it no longer sends messages, and point b has a child node c, so b sends the message to c again. Since point c has no child nodes, the message is no longer sent. So far, b, c, and d all know the elements of other points to point a.

S3.5. After knowing the contribution of all nodes to an element θ, the contribution of a set C to this element can be calculated. When there is a node in the set that contributes negatively to the element, the set contributes negatively to the element, that is, R(C, θ) if and only if When all nodes in the set do not contribute to the element, the set does not contribute to the element, that is, N(C, θ) if and only if When at least one point in the set has a positive contribution to the element and other points do not contribute to the element, the set contributes positively to the element, that is, P(C, θ) if and only if Without loss of generality, we choose a as a specific element. Since R(a, a), P(b, a), P(d, a), N(c, a) are known, C={b} , {d}, {b, c}, {d, c}, {b, d, c}, there is P(C, a), when C={a}, {a, b}, {a, c}, {a, d}, {a, b, c}, {a, b, d}, {a, c, d}, {a, b, c, d}, there is R(C, a ), when C={c}, there is N(C, a).

S3.6, repeat steps S3.2-S3.5 to know the contribution of all nodes to all elements. After node a collects the elements of a, it can collect and broadcast the values of elements b, c, and d for all nodes in turn.

S4, according to the set calculated in step S3, distributedly calculate, for each element θ, a set of contribution of a subset C of nodes with a size of k to it. If C has k nodes and has a positive contribution to the element θ, then record the set of C as P _#k ^-1 (θ), if it is a negative contribution, it is recorded as R _#k ^-1 (θ), if there is no contribution , it is recorded as N _#k ^-1 (θ). and broadcast all messages;

As shown in Figure 6, step S4 includes the following sub-steps:

S4.1, through step S3, knowing the contribution of any node v to an element θ, it is possible to analyze the change of the contribution of this set after v joins a set C. The change of the contribution of the set to the elements is divided into three cases: 1. When the point v has a positive contribution to it, but the set C has no contribution to it, that is, P(v, θ)∧N(C, θ). 2. When the point v contributes negatively to it, and the set C contributes positively to it, that is, R(v, θ)∧P(C, θ). 3. When the point v contributes positively or not to it, and the set C contributes positively to it, that is (P(v, θ)∨N(v, θ))∧P(C, θ). Without loss of generality, we select a as a specific element. It is known that when C={c}, there is N(C, a), and there are P(b, a) and P(d, a), then when b or After d is added to C, the set C changes from no contribution to element a to positive contribution to element a. When C={b}, {d}, {b, d}, P(C, a) and R(a, a) are known, then when a is added to C, the set C is a positive contribution to a becomes a negative contribution. When C={b}, {d}, {b, d}, it is known that there is P(C, a), and there are P(b, a), P(d, a), N(c, a) , when these points are added to C, since C is originally a positive contribution, it is still a positive contribution after adding, but the size of the set changes, so the contribution value will also change.

S4.2, randomly select k nodes from all nodes as a set, and initially k is 1.

S4.3. According to the above three situations, for different elements of each node, use the information collected in step S3 to find the contribution of the set to the element, so as to find MC(C _k , i).

S4.4, set the value of k from 1 to the number of nodes minus 1, and repeat S4.2-S4.3.

S5. According to the result calculated in step S4, each node distributedly calculates its game centrality. Since each point knows the contribution of other points to all elements, each node only needs to distribute the calculation of the contribution value of the set of k nodes selected from other points, and then calculate its game centrality.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (7)

1. A method for solving distributed game centrality, characterized in that, comprising: S1, according to the definition of traditional centrality, divide the graph into a set of elements θ; S2, according to each node in the graph, distribute the contribution information of each node to each element, and the contribution information includes positive contribution, negative contribution and no contribution; S3, according to the contribution information of each node to each element, the contribution information of all nodes to each element in the set is distributed, and the node set P ^-1 (θ) with positive contribution to the element is obtained, and the negative contribution to the element is obtained The node set R ^-1 (θ) of the node set N ^-1 (θ) that does not contribute to the element; S4, according to the node sets P ^-1 (θ), R ^-1 (θ) and N ^-1 (θ), distributedly calculate the contribution information of a node set C with a size of k to the element θ for each element θ , broadcast the contribution information of C to element θ in the graph, so that each node in the graph knows the contribution information of other nodes to all elements; S5, according to the contribution information of each node to each element and the contribution information to each node's distributed computing community, the community is a set of k nodes selected from other nodes, and the contribution change of each node to the community is obtained, and then Get the game centrality of each node. 2. A method for solving distributed game centrality as claimed in claim 1, wherein said traditional centrality is degree centrality, betweenness centrality or closeness centrality. 3. A method for solving distributed game centrality as claimed in claim 2, wherein said traditional centrality is degree centrality or compact centrality, and the specific implementation of said step S1 is: according to degree centrality The definition of degree or close centrality divides the graph into a collection of nodes and treats each node as an element θ. 4. A kind of method for solving distributed game centrality as claimed in claim 2, is characterized in that, described traditional centrality is betweenness centrality, and the concrete realization mode of described step S1 is: according to betweenness centrality Definition, divide the graph into a set of elements θ, each element is a node pair. 5. a kind of distributed game centrality solution method as claimed in claim 1 or 2, is characterized in that, described step S3 comprises: S3.1, according to the contribution information of each node to each element, a breadth-first search tree is distributed in the graph; S3.2, randomly select a node from the graph as the root node of the breadth-first search tree, and the root node distributedly collects the contribution information of each node to each element; obtain the node set P ^-1 ( θ), the node set R ^-1 (θ) that has a negative contribution to the element, and the node set N ^-1 (θ) that does not contribute to the element. 6. a kind of distributed game centrality solution method as claimed in claim 1, is characterized in that, described each node changes to the contribution of group: When the node i contributes positively to the element θ, but the group makes no contribution to the element θ, then the contribution of the node to the group becomes a positive contribution; When node i makes a negative contribution to the element θ, and the group contributes positively to the element θ, the contribution of the node to the group changes as a negative contribution; When node i makes a positive contribution or no contribution to the element θ, and the group makes a positive contribution to the element θ, the contribution of the node to the group changes to no contribution. 7. a kind of distributed game centrality solution method as claimed in claim 1 or 6, is characterized in that, described game centrality is: Among them, ν is the definition of traditional centrality, is the game centrality of node i, k represents the number of nodes, β(k) represents a function related to the size of k, C _k represents a group of size k, represents the expectation of C _k , MC(C _k , i) represents the contribution change of node i to group C _k , and V represents the set of nodes in the graph.