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The metric dimension of a connected graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. We define an extended metric dimension for graphs with some edges missing, which corresponds to the minimum number of vertices in a subset S such that all other vertices have unique distances...
Identifying the source of network diffusion is an important task in applications such as epidemics management and understanding the trend propagation over social networks. As observing each node carries a cost, we study the problem of sequential selection of observed nodes from two aspects: which nodes to observe such that the source is localized with the lowest cost, and for a pre-specified number...
In today's large social and technological networks, since it is unfeasible to observe all the nodes, the source of diffusion is determined based on the observations of a subset of nodes. The probability of source localization error depends on the particular choice of observer nodes. We propose a criterion for observer node selection based on the minimal pairwise Chernoff distance between distributions...
Localizing a source of diffusion is a crucial task in various applications such as epidemics quarantine and identification of trendsetters in social networks. We analyze the problem of selecting the minimum number of observed nodes that would lead to unambiguous source localization, i.e. achieve network observability, when both infection times of all the nodes, as well as the network structure cannot...
In order to quickly curb infections or prevent spreading of rumors, first the source of diffusion needs to be localized. We analyze the problem of source localization, based on infection times of a subset of nodes in incompletely observed tree networks, under a simple propagation model. Our scenario reflects the assumption that having access to all the nodes and full network topology is often not...
Identifying the patient-zero of an epidemic outbreak, locating the person who started a rumor in a social network, finding the computer that initiated the spreading of a computer virus in a network- these are all applications of localizing the source of diffusion in a network. Since most of the networks of interest are very large, we are usually able to observe only a part of the network. In this...
We propose a collaborative, energy efficient method for diffusive source localization in wireless sensor networks. The algorithm is based on distributed and iterative maximum-likelihood (ML) estimation, which is very sensitive to initialization. As a part of the proposed method we present an approach for obtaining a “good enough” initial value for the ML recursion based on infinite time approximation...
Due to limited power resources, energy efficiency is an important aspect of detection in wireless sensor networks. We propose a collaborative detection scheme, based on sequential hypothesis testing, where a randomly chosen node may initiate a collaboration, collecting observations from neighboring nodes to test the hypotheses. Our simulation results show that for large networks and high SNR, the...
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