@article{silva_coverage_2007, 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.}, author = {Silva, Vin de and Ghrist, Robert}, date = {2007}, doi = {10.2140/agt.2007.7.339}, issn = {1472-2747, 1472-2739}, journaltitle = {Algebraic \& Geometric Topology}, keywords = {1 - Networks, 1 - Sensors, 2 - Persistent homology, 3 - Networks, 3 - Sensor, 3 - coordinate-free data}, mrnumber = {MR2308949}, number = {1}, pages = {339--358}, shortjournal = {Algebr. Geom. Topol.}, title = {Coverage in sensor networks via persistent homology}, url = {https://projecteuclid.org/euclid.agt/1513796672}, urldate = {2020-01-18}, volume = {7}, zmnumber = {1134.55003} }