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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For any positive parameter, there is a chain of inclusion maps from a Rips complex to a Čech complex at scaled parameter and back to a Rips complex at scaled parameter.
“R ↩→ C √ 2 ↩→ R √ 2 .”
From Barcodes: the persistent topology of data (2007) · cites this paper as [10]
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- 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
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