Math @ Duke

Publications [#311264] of John Harer
Papers Published
 Munch, E; Shapiro, M; Harer, J, Failure Filtrations for Fenced Sensor Networks
(September, 2011) [1109.6535v1], [doi]
(last updated on 2017/12/13)
Abstract: In this paper we consider the question of sensor network coverage for a
2dimensional domain. We seek to compute the probability that a set of sensors
fails to cover given only nonmetric, local (who is talking to whom)
information and a probability distribution of failure of each node. This builds
on the work of de Silva and Ghrist who analyzed this problem in the
deterministic situation. We first show that a it is part of a slightly larger
class of problems which is #Pcomplete, and thus fast algorithms likely do not
exist unless P$=$NP. We then give a deterministic algorithm which is feasible
in the case of a small set of sensors, and give a dynamic algorithm for an
arbitrary set of sensors failing over time which utilizes a new criterion for
coverage based on the one proposed by de Silva and Ghrist. These algorithms
build on the theory of topological persistence.


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