Volume 7, issue 1 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Coverage in sensor networks via persistent homology

Vin de Silva and Robert Ghrist

Algebraic & Geometric Topology 7 (2007) 339–358
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.

Keywords
Rips complex, Cech complex, persistent homology, sensor network, coverage
Mathematical Subject Classification 2000
Primary: 55M25, 93A15
Secondary: 55N35
References
Publication
Received: 25 November 2005
Revised: 29 January 2006
Accepted: 8 October 2006
Published: 25 April 2007
Authors
Vin de Silva
Department of Mathematics and Computer Science
Pomona College
Claremont CA 91711
USA
Robert Ghrist
Department of Mathematics and Coordinated Sciences Laboratory
University of Illinois
Urbana, IL 61801
USA