On exact covering with unit disks

We study the problem of covering a given point set in the plane by unit disks so that each point is covered exactly once. We prove that 17 points can always be exactly covered. On the other hand, we construct a set of 657 points where an exact cover is not possible.

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Publication Details

Journal
Computational Geometry
Published
2025-03-27
DOI
https://doi.org/10.1016/j.comgeo.2025.102193
Primary Topic
Computational Geometry and Mesh Generation
Type
article
Field-Weighted Citation Impact
0.00

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article

On exact covering with unit disks

Ji Hoon Chun, Sandro Roch, Christian Kipp
Computational Geometry
Computational Geometry and Mesh Generation
article

On exact covering with unit disks

Ji Hoon Chun, Sandro Roch, Christian Kipp
article en

Abstract

We study the problem of covering a given point set in the plane by unit disks so that each point is covered exactly once. We prove that 17 points can always be exactly covered. On the other hand, we construct a set of 657 points where an exact cover is not possible.

Computational GeometryVol. 129
Technische Universität Berlin (DE)
Deutsche Forschungsgemeinschaft
Openalex Percentile: Top 90%
Computational Geometry and Mesh Generation
DOIOpen Access PDFOpenAlex
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On exact covering with unit disks — Ji Hoon Chun, Sandro Roch, et al. · Computational Geometry (2025) | TGRS Research Map | TGRS