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.
%0 Journal Article
%1 deSilva2007Coverage
%A de Silva, V.
%A Ghrist, R.
%D 2007
%J Algebraic and Geometric Topology
%K homology, wsn networks coverage
%P 339--358
%R 10.2140/agt.2007.7.339
%T Coverage in sensor networks via persistent homology
%U http://www.msp.warwick.ac.uk/agt/2007/07/p016.xhtml
%V 7
%X 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{deSilva2007Coverage,
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.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {de Silva, V. and Ghrist, R.},
biburl = {https://www.bibsonomy.org/bibtex/20e10148f6682a00371c8887241b8d8d2/nonancourt},
citeulike-article-id = {3910292},
citeulike-linkout-0 = {http://dx.doi.org/10.2140/agt.2007.7.339},
citeulike-linkout-1 = {http://www.msp.warwick.ac.uk/agt/2007/07/p016.xhtml},
doi = {10.2140/agt.2007.7.339},
interhash = {7f79f3d4e6d76a20dd1993059fe61e9c},
intrahash = {0e10148f6682a00371c8887241b8d8d2},
journal = {Algebraic and Geometric Topology},
keywords = {homology, wsn networks coverage},
pages = {339--358},
posted-at = {2009-01-20 09:53:22},
priority = {2},
timestamp = {2019-08-01T15:35:04.000+0200},
title = {{Coverage in sensor networks via persistent homology}},
url = {http://www.msp.warwick.ac.uk/agt/2007/07/p016.xhtml},
volume = 7,
year = 2007
}