Article,
Coverage in sensor networks via persistent homology
Algebraic and Geometric Topology, (2007)
DOI: 10.2140/agt.2007.7.339
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.
