Algebraic & Geometric Topology

Coverage in sensor networks via persistent homology

Vin de Silva and Robert Ghrist

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Abstract

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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 1 (2007), 339-358.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796672

Digital Object Identifier
doi:10.2140/agt.2007.7.339

Mathematical Reviews number (MathSciNet)
MR2308949

Zentralblatt MATH identifier
1134.55003

Subjects
Primary: 55M25: Degree, winding number 93A15: Large scale systems
Secondary: 55N35: Other homology theories

Keywords
Rips complex Cech complex persistent homology sensor network coverage

Citation

de Silva, Vin; Ghrist, Robert. Coverage in sensor networks via persistent homology. Algebr. Geom. Topol. 7 (2007), no. 1, 339--358. doi:10.2140/agt.2007.7.339. https://projecteuclid.org/euclid.agt/1513796672


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