Interface surfaces for protein-protein complexes
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Coverage and hole-detection in sensor networks via homology
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Extreme Elevation on a 2-Manifold
Discrete & Computational Geometry
Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
International Journal of Robotics Research
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Wireless sensor network survey
Computer Networks: The International Journal of Computer and Telecommunications Networking
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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In this paper we consider the question of sensor network coverage for a two-dimensional domain. We seek to compute the probability that a set of sensors fails to cover given only non-metric, 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 it is part of a slightly larger class of problems which is #P-hard, and thus fast algorithms likely do not exist unless P = NP. The question of whether the specific problem is, in fact, #P-hard remains open. 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 to give an early warning of potential failure. These algorithms build on the theory of topological persistence.