An observer deployment algorithm for locating the diffusion source timely in social network

Locating the source of information diffusion on the social network is a challenging and significant task. It is important to control the spread of wrong information on the social network. An existing method is to observe a few nodes in the network and estimate the location of the source from the data recorded by the observed nodes. The locating effect depends on the positions of the observed nodes. In this paper, we try to find a way to choose the observers that can locate the source earlier. Then we provide a timely observer deployment algorithm to solve the problem. Its basic idea is to use the average distance between every non-observer node and its nearest observer to measure the timeliness of an observers set. We carry out simulation experiments on model networks, the results show that the observers chosen by the algorithm can locate the source more timely. Introduction In recent years, spreading of information through online social networks is ubiquitous [1]. For example, you can discuss the hot topics on micro blog or promote your products through the Internet. But there are also some wrong information, such as computer virus and rumors [2, 3]. An approved way to control the spread of the wrong information is locating the information source timely and accurately [4, 5]. For the huge scale of the online social network, to locate the source by the data recorded by a few observed nodes (this kind of node is called observer) is a feasible method [5, 6, 7]. And the position of the observers in the network has an impact on the performance of the locating method. Prior works on the deployment of observers are mainly about the way to get the highest accuracy of the locating result [8, 9]. However, we know that the sooner we locate the source the less affected by the wrong information. So there is another challenge is to find an observer deployment method to discover the rumor diffusion and locate the source timely. Information diffusion model and locating method Information diffusion model In this paper, the social network is modeled by an undirected graph G={V, E}, V is nodes set, E is edges set. We consider the situation that G is known and there is only one information source in the network. The diffusion model is modeled as Figure 1. In Figure 1(a), the weights on the edges are the diffusion delay (the time of the information go through the edge), o1 and o2 are observers, s is the source, n1 is a usual non-observer. Figure 1(b) shows that a diffusion process starts from s at an unknown time ts. At the time ts , s sends an information m to all its neighbor nodes, when any node first received m, it will send m to all its neighbor nodes except the incoming node (the node which send m to it). The information goes along the weighted shortest paths. The observer needs to record its receiving time and incoming node, but non-observer does not. As shown in Figure 1(b), the diffusion delay of m goes from s to o1 through the path s->o1 is 7, and the path s->n1->o1 is 4+2=6. Because the information goes along the weighted shortest paths, observer o1 received m form n1, not s. So o1 recorded its incoming node is n1 and receiving time is t1. Here t1= ts+6, because ts is unknown, t1 is also unknown. And the information m didn’t go through the edge between s and o1. 2nd Workshop on Advanced Research and Technology in Industry Applications (WARTIA 2016) © 2016. The authors Published by Atlantis Press 1672 Locating method According to the diffusion data recorded by observers, we compute the maximum likelihood estimation to locate the information source. The specific calculation process can be shown as follows: Step 1, get the spread record data of observers that has received the message; Step 2, select a non-observer node s as the root, generating a breadth-first spanning tree; Step 3, assume s as the expected source, computing maximum likelihood estimation ŝ in the generating tree with eq. 1 and eq. 2; ( ) ( ) 1 1 exp 2 ˆ T s s s s d d s μ μ −   − − Λ −     = Λ . (1) [ ] ( ) ( ) ( ) 1 1 2 , 1 1 1 1 , , , k s k i k i p o o k i