Wuqiong Luo

Identifying Infection Sources and Regions in Large Networks

Identifying the infection sources in a network, including the index cases that introduce a contagious disease into a population network, the servers that inject a computer virus into a computer network, or the individuals who started a rumor in a social network, plays a critical role in limiting the damage caused by the infection through timely quarantine of the sources. We consider the problem of estimating the infection sources and the infection regions (subsets of nodes infected by each source) in a network, based only on knowledge of which nodes are infected and their connections, and when the number of sources is unknown a priori. We derive estimators for the infection sources and their infection regions based on approximations of the infection sequences count. We prove that if there are at most two infection sources in a geometric tree, our estimator identifies the true source or sources with probability going to one as the number of infected nodes increases. When there are more than two infection sources, and when the maximum possible number of infection sources is known, we propose an algorithm with quadratic complexity to estimate the actual number and identities of the infection sources. Simulations on various kinds of networks, including tree networks, small-world networks and real world power grid networks, and tests on two real data sets are provided to verify the performance of our estimators.

How to Identify an Infection Source With Limited Observations

A rumor spreading in a social network or a disease propagating in a community can be modeled as an infection spreading in a network. Finding the infection source is a challenging problem, which is made more difficult in many applications where we have access only to a limited set of observations. We consider the problem of estimating an infection source for a Susceptible-Infected model, in which not all infected nodes can be observed. When the network is a tree, we show that an estimator for the source node associated with the most likely infection path that yields the limited observations is given by a Jordan center, i.e., a node with minimum distance to the set of observed infected nodes. We also propose approximate source estimators for general networks. Simulation results on various synthetic networks and real world networks suggest that our estimators perform better than distance, closeness, and betweenness centrality based heuristics .

Finding an infection source under the SIS model

We consider the problem of identifying an infection source based only on an observed set of infected nodes in a network, assuming that the infection process follows a Susceptible-Infected-Susceptible (SIS) model. We derive an estimator based on estimating the most likely infection source associated with the most likely infection path. Simulation results on regular trees suggest that our estimator performs consistently better than the minimum distance centrality based heuristic.

Identifying multiple infection sources in a network

Estimating which nodes are the infection sources that introduce a virus or rumor into a network, or the locations of pollutant sources, plays a critical role in limiting the potential damage to the network through timely quarantine of the sources. In this paper, we derive estimators for the infection sources and their infection regions based on the infection network geometry. We show that in a geometric tree with at most two sources, our estimator identifies these sources with probability going to one as the number of infected nodes increases. We extend and generalize our methods to general graphs, where the number of infection sources are unknown and there may be multiple sources. Numerical results are presented to verify the performance of our proposed algorithms under different types of graph structures.

Estimating infection sources in a network with incomplete observations

We consider the problem of estimating infection sources based on incomplete observations of the set of infected nodes at some point in time, assuming that the infection spreading process follows an Susceptible-Infected (SI) model. We derive an estimator that finds the source nodes associated with the most likely infection path that yields the incomplete observations. Moreover, we design a heuristic algorithm to find the proposed estimator. Simulation results on geometric trees suggest that our estimator performs consistently better than the minimum distance centrality based heuristic.

Identifying infection sources in large tree networks

Estimating which nodes in a network are the infection sources, including the individuals who started a rumor in a social network, the computers that introduce a virus into a computer network, or the index cases of a contagious disease, plays a critical role in identifying the influential nodes in a network, and in some applications, limiting the damage caused by the infection through timely quarantine of the sources. We consider the problem of estimating the infection sources, based only on knowledge of the underlying network connections. We derive estimators based on approximations of the infection sequences counts. We show that if there are at most two infection sources in a geometric tree, our estimator identifies these sources with probability going to one as the number of infected nodes increases. When there are more than two infection sources, we present heuristics that have quadratic complexity. We show through simulations that our proposed estimators can correctly identify the infection sources to within a few hops with high probability.

Infection Spreading and Source Identification: A Hide and Seek Game

The goal of an infection source node (e.g., a rumor or computer virus source) in a network is to spread its infection to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have been infected. We model the infection spreading and source identification problem as a strategic game, where the infection source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that can probe any nodes within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which a Nash equilibrium of the strategic game exists. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.

On the universality of the Jordan center for estimating the rumor source in a social network

We consider the problem of finding the source of a rumor spreading in a social network. We assume that our knowledge of the rumor spreading is limited to the graph topology of the underlying social network and which nodes recently posted the rumor, but not the rates of rumor spreading nor the rumor spreading model. we are interested in finding a source estimator that is applicable to various spreading models, including the Susceptible-Infected (SI), Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Infected (SIRI) models. We show that under all three considered rumor spreading models and with mild technical assumptions, the Jordan center is an optimal rumor source estimator under the most likely infection path criterion. This conclusion applies for a wide range of spreading parameters where nodes may have different infection, recovery and reinfection rates. Since the Jordan center does not depend on the infection, recovery and reinfection rates, it can be regarded as a universal source estimator. Simulation results on various general synthetic networks and real world networks suggest that the Jordan center consistently outperform the distance, closeness, and betweenness centrality based heuristics, even if the network is not a tree.

Rumor Spreading Maximization and Source Identification in a Social Network

The goal of a rumor source node in a social network is to spread its rumor to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have accepted the rumor (which are called infected nodes). We model the rumor spreading and source identification problem as a strategic game, where the rumor source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that probes every node within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the rumor source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which the Nash equilibria of the strategic game exist. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.