Open Access
2007 Coverage in sensor networks via persistent homology
Vin de Silva, Robert Ghrist
Algebr. Geom. Topol. 7(1): 339-358 (2007). DOI: 10.2140/agt.2007.7.339


We introduce a topological approach to a problem of covering a region in Euclidean space by balls of fixed radius at unknown locations (this problem being motivated by sensor networks with minimal sensing capabilities). In particular, we give a homological criterion to rigorously guarantee that a collection of balls covers a bounded domain based on the homology of a certain simplicial pair. This pair of (Vietoris–Rips) complexes is derived from graphs representing a coarse form of distance estimation between nodes and a proximity sensor for the boundary of the domain. The methods we introduce come from persistent homology theory and are applicable to nonlocalized sensor networks with ad hoc wireless communications.


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Vin de Silva. Robert Ghrist. "Coverage in sensor networks via persistent homology." Algebr. Geom. Topol. 7 (1) 339 - 358, 2007.


Received: 25 November 2005; Revised: 29 January 2006; Accepted: 8 October 2006; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1134.55003
MathSciNet: MR2308949
Digital Object Identifier: 10.2140/agt.2007.7.339

Primary: 55M25 , 93A15
Secondary: 55N35

Keywords: Cech complex , coverage , Persistent homology , Rips complex , sensor network

Rights: Copyright © 2007 Mathematical Sciences Publishers

Vol.7 • No. 1 • 2007
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