The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“R ↩→ C √ 2 ↩→ R √ 2 .”
From Barcodes: the persistent topology of data (2007) · cites this paper as [10]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
(2001) · Cited by 5,374
Differential Forms in Algebraic Topology
Bott, R., & Tu, L. W. (1982) · Graduate texts in mathematics · doi:10.1007/978-1-4757-3951-0 · Cited by 2,860
Gromov, M. (1987) · Mathematical Sciences Research Institute Publications · doi:10.1007/978-1-4613-9586-7_3 · Cited by 1,817
Coverage problems in wireless ad-hoc sensor networks
Meguerdichian, S., Koushanfar, F., Potkonjak, M., & Srivastava, M. B. (2002) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infcom.2001.916633 · Cited by 1,698
Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591
Maintaining Sensing Coverage and Connectivity in Large Sensor Networks
Zhang, H., & Hou, J. C. (2005) · Auerbach Publications eBooks · doi:10.1201/9780203323687.ch28 · Cited by 1,509
The Number of Neighbors Needed for Connectivity of Wireless Networks
Xue, F., & Kumar, P. R. (2004) · Wireless Networks · doi:10.1023/b:wine.0000013081.09837.c0 · Cited by 834
Geographic routing without location information
Rao, A., Ratnasamy, S., Papadimitriou, C. H., Shenker, S. J., & Stoica, I. G. (2003) · ACM Annual International Conference on Mobile Computing and Networking (MobiCom) · doi:10.1145/938985.938996 · Cited by 756
Topological persistence and simplification
Edelsbrunner, H., Letscher, D., & Zomorodian, A. J. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2000.892133 · Cited by 716
Coverage in wireless ad hoc sensor networks
Li, X., Wan, P., & Frieder, O. (2003) · IEEE Transactions on Computers · doi:10.1109/tc.2003.1204831 · Cited by 523
Flagged first, then by citations
Research works printed but not linked: 8
- Allili, 2001, IEEE Intl. Conf. Image Proc., 173
- Silva, 2004, Symp. Point-Based Graphics
- Silva, 2005, Robotics: Systems and Science
- Hausmann, 1995, Prospects in topology (Princeton, NJ, 1994), 138, 175
- Koskinen, 2004, Proceedings of 16th ITC Specialist Seminar, 11
- Meguerdichian, 2001, IEEE INFOCOM, 1380
- Rao, 2003, Proceedings of 9th Annual International Conference on Mobile Computing and Networking (Mobicom’03)
- Zhang, 2004, International Workshop on Theoretical and Algorithmic Aspects of Sensor, Ad hoc Wireless and Peer-to-Peer Networks
Cited by
Sorted by citations
Items 401–421 of 421
Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.001
Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.004
Distance to Probability Measures
Boissonnat, J., Chazal, F., & Yvinec, M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108297806.011
Estimating the Coverage Measure and the Area Explored by a Line-Sweep Sensor on the PlanePreprint
Vianna, M. L. C., Goubault, É., Jaulin, L., & Putot, S. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4578550
Topology-enhanced machine learning for speech signal processing
Feng, P., Qu, Q., Zhang, H., Yi, S., Yu, Z., Ding, Z., & Zhu, Y. (2026) · Nature Communications · doi:10.21203/rs.3.rs-3978261/v1
Topo-Geometric Analysis of Variability in Point Clouds Using Persistence Landscapes
Matuk, J., Kurtek, S., & Bharath, K. (2024) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2024.3451328
Can We Determine Whether a Set of Ethereum Transaction Data Contains Fraudulent Transactions?
Nakatani, S., Kuzuno, H., Takita, M., Mohri, M., & Shiraishi, Y. (2024) · IEEE Conference on Dependable and Secure Computing (DSC) · doi:10.1109/dsc63325.2024.00023
He, Y., Wu, J., & Li, M. Z. (2025) · Chinese Physics B · doi:10.1088/1674-1056/ae1457
Dynamical and topological tools for (modern) music analysis
Bergomi, M. G. (2015) · theses.fr (ABES) · doi:10.70675/7f9d64bezcdc1z4ecbza15fzf3aac6e60bfe · Cited by 12
Approche topologique de la métrologie du mouvement pour des applications en réalité virtuelle
Bensekka, C. A. (2018) · theses.fr (ABES) · doi:10.70675/db7e889ezda81z473bz87c4z72e64e934169
Bajracharya, E. (2026) · Research Square · doi:10.21203/rs.3.rs-9408940/v1
Context-aware subregion-wise patching for effective brain tumor segmentation in 3D MRI scans
Asghar, M., & Shahid, A. R. (2026) · PeerJ Computer Science · doi:10.7717/peerj-cs.3768
Incremental Critical Cells for Homology Characterization
Malott, N. O., Yadav, A., & Wilsey, P. A. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-21477-5_3
D-BTC: A Simply Connected Two-Dimensional Blockchain Protocol
Bloundi, S., & Ben-Azza, H. (2026) · Blockchains · doi:10.3390/blockchains4020007
Topological control of singlet fission
Riemersma, K., Gautam, K., Solis, A. F., Tran, T. B. M., & Rolczynski, B. S. (2026) · The Journal of Chemical Physics · doi:10.1063/5.0339622
Evaluating Cooling-Center Coverage Using Persistent Homology of a Filtered Witness Complex
O'Neil, E., & Tymochko, S. (2026) · SIAM Journal on Applied Mathematics · doi:10.1137/25m1741145
Martinez, D. A. S., Razmarashooli, A., Chua, Y. K., Panthi, A., Okumu, M., Hu, C., Schrader, P. T., Downey, A. R. J., Comert, G., Begashaw, N., et al. (2026) · Measurement Science and Technology · doi:10.1088/1361-6501/aea4d7
Alsulami, S. (2026) · AIMS Mathematics · doi:10.3934/math.20261180
Shymkovych, V., & Hryshyn, O. (2026) · International Journal of Data Science and Analytics · doi:10.1007/s41060-026-01304-5
Geometric Optimization in Wireless Networks
Wu, W., & Zhang, Z. (2013) · Springer eBooks · doi:10.1007/978-1-4419-7997-1_41
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 ›
Are you an author, or do you see a problem with this page? Request a review
