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Coverage in sensor networks via persistent homology
Open accessAbstract
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.
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Metadata
- Authors
- de Silva, V., & Ghrist, R.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Venue
- Algebraic & Geometric Topology
- Publisher
- Mathematical Sciences Publishers
- Published
- 2007-04-25
- Volume
- 7
- Issue
- 1
- Pages
- 339-358
- ISSN
- 1472-2739 (ISSN-L)
- 1472-2747
- OpenAlex
- W2153986241
- Cited by
- 422
- References
- 24
- Citations by year
- 2026: 10 · 2025: 11 · 2024: 22 · 2023: 15 · 2022: 24 · 2021: 30 · 2020: 25 · 2019: 38 · 2018: 41 · 2017: 33 · 2016: 15 · 2015: 18 · 2014: 26 · 2013: 25 · 2012: 24
- FWCI
- 18.64
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Algebraic & Geometric Topology (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Funders
- National Science Foundation
- Defense Advanced Research Projects Agency
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Keywords
- covering problems, sensor networks, persistent homology, Vietoris-Rips complex, ball covering, proximity sensors, ad hoc networks, distance estimation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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