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CN115842741A - Method for evaluating cluster information propagation capacity under peer-to-peer network - Google Patents

Method for evaluating cluster information propagation capacity under peer-to-peer network Download PDF

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CN115842741A
CN115842741A CN202211446578.0A CN202211446578A CN115842741A CN 115842741 A CN115842741 A CN 115842741A CN 202211446578 A CN202211446578 A CN 202211446578A CN 115842741 A CN115842741 A CN 115842741A
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information
receiving node
information receiving
peer
source information
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王艺欣雨
李铁术
谭蓉俊
李斌
莫剑飞
江雨珊
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No 750 Test Field of China Shipbuilding Industry Corp
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Abstract

The invention discloses a method for evaluating cluster information propagation capacity in a peer-to-peer network, wherein the peer-to-peer network comprises the following steps: the cluster formed by the nodes carries out information interaction through a peer-to-peer network, and the nodes comprise: the controller triggers the first information receiving node to generate information F w (1) And recording the time t for sending information by the first information receiving node 1 And each node receives time t Harvesting machine The peer-to-peer network appoints a single-source information receiving node and a multi-source information receiving node to send out information F at the time of delay time dt after receiving the information w (n), dt is the forwarding period, n is the forwarding times, the information propagation efficiency eta of the forwarding node is calculated by a formula,
Figure DDA0003950594160000011

Description

在对等网络下的集群信息传播能力的评估方法Evaluation Method of Cluster Information Propagation Capability in Peer-to-Peer Network

技术领域technical field

属于信息传播算法及评估算法领域,尤其涉及一种在对等网络下集群的信息传播能力校验及分析评估算法。The invention belongs to the field of information dissemination algorithms and evaluation algorithms, and in particular relates to an information dissemination ability verification and analysis evaluation algorithm of a cluster under a peer-to-peer network.

背景技术Background technique

信息传播是集群协同执行任务的重要支撑之一。信息传播的方式有限网络、枚举网络、无中心对等网络等模式,由于无中心对等模式基于网络拓扑,所有节点为对等结构,具有简单、灵活、易扩展等特点,在集群信息传播中是一种非常重要的模式。在这种模式下,各节点通过与相邻对等节点的连接遍历整个网络,节点间直接进行信息交互,实现信息对等、信息内聚、角色对等,大幅提升了资源共享和信息传递的效率。Information dissemination is one of the important supports for clusters to perform tasks collaboratively. The mode of information dissemination is limited network, enumeration network, non-central peer-to-peer network and other modes. Since the non-central peer-to-peer mode is based on network topology, all nodes are peer-to-peer structures, which are simple, flexible, and easy to expand. In the cluster information dissemination Medium is a very important pattern. In this mode, each node traverses the entire network by connecting with adjacent peer nodes, and the nodes directly interact with each other to achieve information equivalence, information cohesion, and role equivalence, which greatly improves the efficiency of resource sharing and information transmission. efficiency.

然而无中心对等模式带来的集群信息传播的涌现性效应,使得集群信息传播处理及校验方法缺失,难以量化评估,传播网络中的薄弱点或阻碍点难以确定。However, the emergence effect of cluster information dissemination brought about by the decentralized peer-to-peer model makes cluster information dissemination processing and verification methods lacking, making it difficult to quantify and evaluate, and it is difficult to determine weak points or obstacles in the communication network.

发明内容Contents of the invention

本发明为了解决在对等网络下集群信息传播能力难以验证与评估的问题,本申请的发明目的是提供一种在对等网络下集群的信息传播能力校验及分析评估算法,通过一种在集群内各节点信息分配拓展算法,对数字信号的简单编码,解耦涌现性,实现对集群传播能力的验证和传播效率的量化评估。In order to solve the problem that it is difficult to verify and evaluate the information dissemination ability of the cluster under the peer-to-peer network, the purpose of the invention of this application is to provide a verification and analysis evaluation algorithm for the information dissemination ability of the cluster under the peer-to-peer network. The information distribution and expansion algorithm of each node in the cluster, simple encoding of digital signals, decoupling of emergence, and realization of the verification of cluster communication capabilities and quantitative evaluation of communication efficiency.

为了完成本申请的发明目的,本申请采用以下技术方案:In order to complete the invention purpose of the application, the application adopts the following technical solutions:

本发明的一种在对等网络下的集群信息传播能力的评估方法,对等网络包括:m个节点和控制器,其中m≥3,各节点组成一个集群,它们通过对等网络进行信息交互,节点包括:首发信息接收节点、单源信息接收节点和多源信息接收节点,控制器触发首发信息接收节点产生信息Fw(1)并且记录首发信息接收节点发送信息的时间t1和各个节点的接收时间t,对等网络约定单源信息接收节点和多源信息接收节点在接收信息后的延时时间dt时刻发出上述信息Fw(n),dt为转发周期,n为信息校验值即为转发次数,若单源信息接收节点和多源信息接收节点此前不存在上述信息Fw(n),则Fw(n)视为有效接收量,其中:A method for evaluating cluster information dissemination capability under a peer-to-peer network of the present invention, the peer-to-peer network includes: m nodes and controllers, wherein m≥3, each node forms a cluster, and they exchange information through the peer-to-peer network , the nodes include: the first information receiving node, the single-source information receiving node and the multi-source information receiving node, the controller triggers the first information receiving node to generate information F w (1) and records the time t 1 and each node receiving time t, the peer-to-peer network agrees that the single-source information receiving node and the multi-source information receiving node send the above information F w (n) at the delay time dt after receiving the information, where dt is the forwarding cycle and n is the information verification The value is the number of forwarding times. If the above-mentioned information F w (n) does not exist before the single-source information receiving node and the multi-source information receiving node, then F w (n) is regarded as the effective receiving amount, where:

(a)、首发信息接收节点向外广播信息Fw(1)(a), the first information receiving node broadcasts information F w (1)

当对等网络中不存在信息时,信息校验值n=0;控制器在t1时刻触发一个首发信息接收节点发送一条信息,首发信息接收节点信息将Fw(n)的信息校验值n=0变为n=1,并向外广播信息Fw(1);When there is no information in the peer-to-peer network, the information check value n=0; the controller triggers a first message receiving node to send a message at time t1 , and the first message receiving node information will be the information check value of F w (n) n=0 becomes n=1, and broadcasts information F w (1);

(b)、单源信息接收节点信息处理转发机制(b), Single-source information receiving node information processing and forwarding mechanism

假设单源信息接收节点在t至t+dt时段仅收到信息Fw(n),在t至t+dt时段,单源信息接收节点此前不存在上述信息Fw(n),则单源信息接收节点将Fw(n)中校验值n变为1+n,n为2,3,4……;并且在t+dt时刻将信息Fw(n+1)向外广播;Assuming that the single-source information receiving node only receives the information F w (n) during the period from t to t + dt, and the single -source information receiving node does not have the above information F w (n) before the period from t to t + dt , then the single-source information receiving node changes the check value n in F w (n) to 1+n, n is 2, 3, 4... ; broadcast outward;

(c)、多源信息接收节点信息处理转发机制(c), multi-source information receiving node information processing and forwarding mechanism

若多源信息接收节点在t至t+dt时段,首次接收到几个Fw(n-1)、Fw(n)、Fw(n+1)……相同的信息,比较n-1、n、n+1……校验值的大小,则多源信息接收节点将最小校验值+1后,在t至t+dt时刻将信息Fw(n)向外广播,n为最小校验值+1,即上述多源信息接收节点(Zk)的转发级数,n为2,3,4……;If the multi-source information receiving node receives several F w (n-1), F w (n), F w (n+1)... the same information for the first time during the period from t to t + dt, compare n -1, n, n+1... the size of the check value, the multi-source information receiving node will broadcast the information Fw(n) to the outside at the time t received to t received + dt after the minimum check value + 1, n is the minimum check value + 1, that is, the number of forwarding stages of the above-mentioned multi-source information receiving node (Z k ), n is 2, 3, 4...;

(d)、计算信息传播效率η(d), calculate the information dissemination efficiency η

单源信息接收节点和多源信息接收节点的信息传播效率η通过式(1)计算,The information propagation efficiency η of single-source information receiving node and multi-source information receiving node is calculated by formula (1),

Figure BDA0003950594140000021
Figure BDA0003950594140000021

式中n为单源信息接收节点和多源信息接收节点广播出去的校验值,即转发次数;In the formula, n is the check value broadcast by the single-source information receiving node and the multi-source information receiving node, that is, the number of forwarding times;

m为集群节点总数;m is the total number of cluster nodes;

Δt为信息传播总时延,Δt=t+dt-t1,t为单源信息接收节点或多源信息接收节点接收信息的时间,t1为首发信息接收节点发送信息的时间,dt为转发周期;Δt is the total delay of information dissemination, Δt= t +dt-t 1 , t is the time for single-source information receiving node or multi-source information receiving node to receive information, t 1 is the time for the first information receiving node to send information, dt is the forwarding cycle;

信息传播效率η值越小的节点,说明其传播能力越强。The smaller the value of information dissemination efficiency η is, the stronger its dissemination ability is.

本发明的在对等网络下的集群信息传播能力的评估方法,其中:有效接收量为此前没有接收到的信息。In the method for evaluating the cluster information dissemination capability under the peer-to-peer network of the present invention, the effective received amount is information that has not been received before.

本发明的在对等网络下的集群信息传播能力的评估方法,其中:在步骤(b)和步骤(c)中,如果此前已经存在上述信息Fw(n)时,首发信息接收节点、单源信息接收节点和多源信息接收节点对上述信息Fw(n)不广播。The method for evaluating cluster information dissemination capability under the peer-to-peer network of the present invention, wherein: in step (b) and step (c), if the above-mentioned information F w (n) has existed before, the first information receiving node, unit The source information receiving node and the multi-source information receiving node do not broadcast the above information F w (n).

本发明的在对等网络下的集群信息传播能力的评估方法具有以下优点:The evaluation method of the cluster information dissemination capability under the peer-to-peer network of the present invention has the following advantages:

(1)、该方法的应用不受限于集群节点信息传输构型,可应用于链式、星型网络,尤其适用于无中心对等网络;(1) The application of this method is not limited to the cluster node information transmission configuration, and can be applied to chain and star networks, especially suitable for decentralized peer-to-peer networks;

(2)、该方法的应用不受限于集群节点个数及信息分发传输级数。(2) The application of this method is not limited to the number of cluster nodes and the number of information distribution and transmission stages.

(3)、该方法的应用不受限于指定指控端和接收端,集群内各节点可为双工模式,指控端和接收端可以是集群内任意节点。(3) The application of this method is not limited to specifying the pointing end and receiving end, each node in the cluster can be in duplex mode, and the pointing end and receiving end can be any node in the cluster.

(4)、该方法的应用不受限于信息传播的方向,信息可全向收发。(4) The application of this method is not limited to the direction of information propagation, and information can be sent and received in all directions.

(5)、对于信息传播效率η,值越小则说明传播效率越高。(5) For information dissemination efficiency η, the smaller the value, the higher the dissemination efficiency.

(6)、若想改善信息传播效率,可通过改变集群节点布设态势以达到信息转发级数,以及降低多级传播时延的方式。(6) If you want to improve the efficiency of information dissemination, you can change the layout of cluster nodes to achieve the number of information forwarding stages and reduce the multi-stage propagation delay.

(7)、该传播方法通过数字信号的简单编码运算实现对等网络下集群信息传播涌现性解耦,可作为一种信息传播分配算法及传播校验算法,具有较好的灵活性、普适性。(7) The propagation method realizes the emergent decoupling of cluster information propagation under the peer-to-peer network through simple coding operations of digital signals, and can be used as an information propagation distribution algorithm and propagation verification algorithm, with good flexibility and universal application sex.

(8)、该信息传播效率方法不受限于集群规模,实现对传播效率的量化计算,方法简便;还可用于实现对信息传播效率的改进提升。(8) The information dissemination efficiency method is not limited to the size of the cluster, and the quantitative calculation of the dissemination efficiency is realized, and the method is simple; it can also be used to improve the information dissemination efficiency.

(9)、本发明增加了信息校验值,可以有效地记录转发次数。(9), the present invention increases the check value of the information, which can effectively record the times of forwarding.

附图说明Description of drawings

图1为本发明的在对等网络下的集群信息传播能力的评估方法中节点和控制器之间关系的示意图。FIG. 1 is a schematic diagram of the relationship between nodes and controllers in the method for evaluating cluster information dissemination capability under a peer-to-peer network according to the present invention.

在图1中,标号1为控制器;标号2为节点;标号Zw为首发信息接收节点;标号Zj为单源信息接收节点;Zk为多源信息接收节点。In Figure 1, the label 1 is the controller; the label 2 is the node; the label Z w is the first information receiving node; the label Z j is the single-source information receiving node; Z k is the multi-source information receiving node.

具体实施方式Detailed ways

为了清楚起见,首先对首发信息接收节点、单源信息接收节点和多源信息接收节点进行定义。For the sake of clarity, the initial information receiving node, single-source information receiving node and multi-source information receiving node are defined first.

首发信息接收节点是指信息产生源节点或该网络首次接收某一信息的节点。The first information receiving node refers to the information generation source node or the node that the network receives a certain information for the first time.

单源信息节点是指,在某一时段内,仅收到一条信息的节点。A single-source information node refers to a node that only receives one piece of information within a certain period of time.

多源信息节点是指,在某一时段内,收到多条信息的节点。A multi-source information node refers to a node that receives multiple pieces of information within a certain period of time.

首发信息接收节点、单源信息节点和多源信息节点是随机的,它们不是某个指定的节点,在集群中首发信息接收节点为一个,单源信息节点和多源信息节点可以是一个或多个。First information receiving node, single-source information node and multi-source information node are random, they are not a specified node, there is only one first information receiving node in the cluster, single-source information node and multi-source information node can be one or more indivual.

如图1所示,本发明对等网络包括:m个节点2和控制器1,其中m≥3,各节点2组成一个集群,它们通过对等网络进行信息交互,为了以下叙述的方便,将节点人为地分成三类,即节点2包括:首发信息接收节点Zw、单源信息接收节点Zj和多源信息接收节点Zk,控制器1触发首发信息接收节点Zw产生信息Fw(1)并且记录首发信息接收节点发送信息的时间t1和各个节点的接收时间t,对等网络约定单源信息接收节点Zj和多源信息接收节点Zk在接收信息后的延时时间dt时刻发出上述信息Fw(n),dt为转发周期,n为信息校验值即为转发次数,若单源信息接收节点Zj和多源信息接收节点Zk此前不存在上述信息Fw(n),则Fw(n)视为有效接收量,本发明的在对等网络下的集群信息传播能力的评估方法包括以下步骤:As shown in Figure 1, the peer-to-peer network of the present invention includes: m nodes 2 and a controller 1, wherein m≥3, and each node 2 forms a cluster, and they perform information exchange through the peer-to-peer network. For the convenience of the following description, the The nodes are artificially divided into three categories, that is, node 2 includes: the first information receiving node Z w , the single-source information receiving node Z j and the multi-source information receiving node Z k , and the controller 1 triggers the first information receiving node Z w to generate information F w ( 1) and record the time t1 when the first information receiving node sends the information and the receiving time t of each node, and the peer-to-peer network agrees on the delay time after the single-source information receiving node Z j and the multi-source information receiving node Z k receive the information The above information F w (n) is sent out at time dt, dt is the forwarding period, and n is the information check value, which is the number of forwarding times. If the single-source information receiving node Z j and the multi-source information receiving node Z k do not have the above-mentioned information F w before (n), then Fw (n) is regarded as effective reception amount, the evaluation method of the cluster information dissemination capability under the peer-to-peer network of the present invention comprises the following steps:

(a)、首发信息接收节点Zw向外广播信息Fw(1)(a), the initial information receiving node Z w broadcasts information F w (1)

当对等网络中不存在信息时,信息校验值n=0;控制器1在t1时刻触发一个首发信息接收节点Zw发送一条信息,首发信息接收节点Zw信息将Fw(n)的信息校验值n=0变为n=1,并向外广播信息Fw(1);When there is no information in the peer-to-peer network, the information check value n=0; the controller 1 triggers a first information receiving node Zw to send a piece of information at time t1 , and the information of the first information receiving node Zw will be Fw (n) The information check value n=0 becomes n=1, and the information F w (1) is broadcast to the outside;

(b)、单源信息接收节点Zj信息处理转发机制(b), single-source information receiving node Z j information processing and forwarding mechanism

假设单源信息接收节点Zj在t至t+dt时段仅收到信息Fw(n),在t至t+dt时段,单源信息接收节点Zj此前不存在上述信息Fw(n),则单源信息接收节点Zj将Fw(n)中校验值n变为1+n,n为2,3,4……;并且在t+dt时刻将信息Fw(n+1)向外广播;Assuming that the single-source information receiving node Z j only receives information F w (n) during the period from t to t + dt, and the single-source information receiving node Z j does not have the above information F before the period from t to t + dt w (n ) , then the single-source information receiving node Z j changes the check value n in F w (n) to 1+n, where n is 2, 3, 4...; w (n+1) broadcasts outward;

(c)、多源信息接收节点Zk信息处理转发机制(c), multi-source information receiving node Z k information processing and forwarding mechanism

若多源信息接收节点Zk在t至t+dt时段,首次接收到几个Fw(n-1)、Fw(n)、Fw(n+1)……相同的信息,比较n-1、n、n+1……校验值的大小,则多源信息接收节点Zk将最小校验值+1后,在t至t+dt时刻将信息Fw(n)向外广播,n为最小校验值+1,即上述多源信息接收节点Zk的转发级数,n为2,3,4……;If the multi-source information receiving node Z k receives several Fw (n-1), Fw (n), Fw (n+1)... the same information for the first time during the period from t to t+dt, Comparing the size of n-1, n, n+1... check value, the multi-source information receiving node Z k will add the minimum check value + 1, and send the information Fw(n) from t to t+dt Outward broadcast, n is the minimum check value + 1, that is, the number of forwarding stages of the above-mentioned multi-source information receiving node Z k , n is 2, 3, 4...;

(d)、计算信息传播效率η(d), calculate the information dissemination efficiency η

单源信息接收节点Zj和多源信息接收节点Zk的信息传播效率η通过式(1)计算,The information propagation efficiency η of the single-source information receiving node Z j and the multi-source information receiving node Z k is calculated by formula (1),

Figure BDA0003950594140000041
Figure BDA0003950594140000041

式中n为单源信息接收节点Zj和多源信息接收节点Zk广播出去的校验值,即转发次数;In the formula, n is the check value broadcast by the single-source information receiving node Z j and the multi-source information receiving node Z k , that is, the number of forwarding times;

m为集群节点总数;m is the total number of cluster nodes;

Δt为信息传播总时延,Δt=t+dt-t1,t为单源信息接收节点Zj或多源信息接收节点Zk的接收信息的时间,t1为首发信息接收节点Zw发送信息的时间,dt为转发周期;Δt is the total time delay of information dissemination, Δt=t received +dt-t 1 , t received is the time of receiving information from single-source information receiving node Z j or multi-source information receiving node Z k , t 1 is the first information receiving node Z w The time to send information, dt is the forwarding cycle;

信息传播效率η值越小的节点2说明其传播能力越强。The smaller the value of information dissemination efficiency η, the node 2 indicates that its dissemination ability is stronger.

在步骤(b)和步骤(c)中,如果此前已经存在上述信息Fw(n)时,首发信息接收节点Zw、单源信息接收节点Zj和多源信息接收节点Zk对上述信息Fw(n)不广播。当一个多源信息接收节点Zk转发信息后,首发信息接收节点Zw、单源信息接收节点Zj和其它多源信息接收节点Zk会又接收到转发信息,但是,因为首发信息接收节点Zw、单源信息接收节点Zj和多源信息接收节点Zk已经存在上述信息Fw(n),首发信息接收节点Zw、单源信息接收节点Zj和多源信息接收节点Zk对上述信息Fw(n)不广播,也不再计算上述首发信息接收节点Zw、单源信息接收节点Zj和多源信息接收节点Zk的信息传播效率η。In step (b) and step (c), if the above-mentioned information F w (n) already existed before, the initial information receiving node Z w , the single-source information receiving node Z j and the multi-source information receiving node Z k F w (n) does not broadcast. When a multi-source information receiving node Z k forwards the information, the first information receiving node Z w , the single-source information receiving node Z j and other multi-source information receiving nodes Z k will receive the forwarding information again, but, because the first information receiving node Z w , single-source information receiving node Z j and multi-source information receiving node Z k already have the above information F w (n), the first information receiving node Z w , single-source information receiving node Z j and multi-source information receiving node Z k The above information F w (n) is not broadcast, and the information propagation efficiency η of the above-mentioned initial information receiving node Z w , single-source information receiving node Z j and multi-source information receiving node Z k is no longer calculated.

本发明还可以有其他多种实施例,在不背离本发明精神及其实质的情况下,熟悉本领域的技术人员可以根据本发明作出各种相应的改变和变形,但这些改变和变形都应属于本发明的权利要求的保护范围。The present invention can also have other multiple embodiments, without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these changes and deformations should Belong to the protection scope of the claims of the present invention.

Claims (3)

1. A method for evaluating the propagation capacity of cluster information in a peer-to-peer network, the peer-to-peer network comprising: m nodes (2) and a controller (1), wherein m is more than or equal to 3, each node (2) forms a cluster, and the nodes carry out information interaction through a peer-to-peer network, and the nodes (2) comprise: first-sending information receiving node (Z) w ) Single source information receiving node (Z) j ) And a multi-source information receiving node (Z) k ) The controller (1) triggers the first information receiving node (Z) w ) Generating information F w (1) And recording the time t of sending information by the first information receiving node 1 And reception time t of each node Harvesting machine Peer-to-peer network promises a single source information receiving node (Z) j ) And a multi-source information receiving node (Z) k ) At receiving messageSending the information F at the time point of delay time dt after rest w (n), dt is the forwarding period, n is the information check value, namely the forwarding times, if the single source information receiving node (Z) j ) And a multi-source information receiving node (Z) k ) The information F does not exist before w (n) then F w (n) as an effective receiving amount, characterized in that:
(a) First sending information receiving node (Z) w ) Broadcasting out information F w (1)
When no information exists in the peer-to-peer network, the information check value n =0; the controller (1) is at t 1 Triggering an initial message receiving node (Z) at a time w ) Sending a message, first message receiving node (Z) w ) Information will F w The information check value n =0 of (n) becomes n =1, and the information F is broadcasted to the outside w (1);
(b) Single source information receiving node (Z) j ) Information handling forwarding mechanism
Suppose a single source information receiving node (Z) j ) At t Harvesting machine To t Harvesting machine The + dt period receives only information F w (n) at t Harvesting machine To t Harvesting machine + dt periods, in which the single-source information receiving node (Z) has not previously existed the above-mentioned information F w (n), then the single source information receiving node (Z) j ) F is to be w In (n), check value n is 1+ n, n is 2,3,4 \8230; and at t Harvesting machine + dt time will information F w (n + 1) broadcasting outwards;
(c) Multi-source information receiving node (Z) k ) Information handling forwarding mechanism
If the multi-source information receiving node (Z) k ) At t Harvesting machine To t Harvesting machine A + dt period, first receiving several F w (n-1)、F w (n)、F w (n + 1) \8230; same information, comparing n-1, n +1 \8230; check value size, then multi-source information receiving node (Z) k ) After the minimum check value +1, at t Harvesting machine To t Harvesting machine + dt time will information F w (n) is broadcast outwards, n is the minimum check value +1, namely the multi-source information receiving node (Z) k ) The forwarding level of the network is 2,3,4, 8230, 8230;
(d) Calculating information propagation efficiency eta
Single source information receiving node (Z) j ) And a multi-source information receiving node (Z) k ) The information propagation efficiency η of (a) is calculated by the equation (1),
Figure FDA0003950594130000011
wherein n is a single source information receiving node (Z) j ) And a multi-source information receiving node (Z) k ) Broadcasting the check value, namely the forwarding times;
m is the total number of the cluster nodes;
Δ t is total time delay of information propagation, Δ t = t Harvesting machine +dt-t 1 ,t Harvesting machine As a single source information receiving node (Z) j ) Or a multi-source information receiving node (Z) k ) Time of receiving information, t 1 For the first message receiving node (Z) w ) The time of sending information, dt is the forwarding period;
the smaller the value of the information propagation efficiency eta is, the stronger the propagation capacity of the node (2) is.
2. The method for evaluating the cluster information dissemination ability under a peer-to-peer network according to claim 1, wherein: the effective received amount is information that was not received before this.
3. The method for evaluating the cluster information dissemination ability under a peer-to-peer network according to claim 2, wherein: in the steps (b) and (c), if the above-mentioned information F has existed before w (n) first message receiving node (Z) w ) Single source information receiving node (Z) j ) And a multi-source information receiving node (Z) k ) For the above information F w (n) not broadcast.
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