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We study the problem of identifying multiple rumor or infection sources in a network under the susceptible-infected model, and where these sources may start infection spreading at different times. We introduce the notion of an abstract estimator that, given the infection graph, assigns a higher value to each vertex in the graph it considers more likely to be a rumor source. This includes several of the single-source estimators developed in the literature. We introduce the concepts of a quasi-regular tree and a heavy center, which allows us to develop an algorithmic framework that transforms an abstract estimator into a two-source joint estimator, in which the infection graph can be thought of as covered by overlapping infection regions. We show that our algorithm converges to a local optimum of the estimation function if the underlying network is a quasi-regular tree. We further extend our algorithm to more than two sources, and heuristically to general graphs. Simulation results on both synthetic and real-world networks suggest that our algorithmic framework outperforms several existing multiple-source estimators, which typically assume that all sources start infection spreading at the same time. [ABSTRACT FROM PUBLISHER]

We formulate and study a multi-user multi-armed bandit problem that exploits the temporal–spatial opportunistic spectrum access (OSA) of primary user (PU) channels, so that secondary users (SUs) who do not interfere with each other can make use of the same PU channel. We first propose a centralized channel allocation policy that has logarithmic regret, but requires a central processor to solve an NP-complete optimization problem at exponentially increasing time intervals. To overcome the high computation complexity at the central processor, we also propose heuristic distributed policies that, however, have linear regrets. Our first distributed policy utilizes a distributed graph coloring and consensus algorithm to determine SUs’ channel access ranks, while our second distributed policy incorporates channel access rank learning in a local procedure at each SU at the cost of a higher regret. We compare the performance of our proposed policies with other distributed policies recently proposed for temporal (but not spatial) OSA. We show that all these policies have linear regrets in our temporal–spatial OSA framework. Simulations suggest that our proposed policies have significantly smaller regrets than the other policies when spectrum temporal–spatial reuse is allowed. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, gSPAWN allows sensors to broadcast a message whose size does not depend on the network size or density, making it more suitable for applications in wireless sensor networks. We show that gSPAWN converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of gSPAWN to a network localization problem in non-line-of-sight environments. Numerical results suggest that gSPAWN converges much faster in general than the diffusion method, and has lower communication costs per sensor, with comparable root-mean-square errors. [ABSTRACT FROM PUBLISHER]