Convex Covering Using Collections of Convex Polygons and Set Cover

In the convex covering problem, we are given a convex polygon with holes P and the goal is to cover P using a small number of convex polygons that lie inside P. In this paper, we solve the problem using the following strategy. We find a big collection of large (often maximal) convex polygons inside P and then solve several set cover problems to find a small subset of the collection that covers the whole polygon. The quality of our heuristics is confirmed by winning the second place in the CG:SHOP 2023 Challenge.

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Publication Details

Journal
Computing in Geometry and Topology
Published
2024-10-11
DOI
https://doi.org/10.57717/cgt.v5i4.77
Primary Topic
Computational Geometry and Mesh Generation
Type
article
Field-Weighted Citation Impact
0.00
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article

Convex Covering Using Collections of Convex Polygons and Set Cover

Computing in Geometry and Topology
Computational Geometry and Mesh Generation
article

Convex Covering Using Collections of Convex Polygons and Set Cover

article en

Abstract

In the convex covering problem, we are given a convex polygon with holes P and the goal is to cover P using a small number of convex polygons that lie inside P. In this paper, we solve the problem using the following strategy. We find a big collection of large (often maximal) convex polygons inside P and then solve several set cover problems to find a small subset of the collection that covers the whole polygon. The quality of our heuristics is confirmed by winning the second place in the CG:SHOP 2023 Challenge.

Computing in Geometry and Topology
Aix-Marseille Université (FR)
Openalex Percentile: Top 31%
Computational Geometry and Mesh Generation
DOIOpen Access PDFOpenAlex
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Convex Covering Using Collections of Convex Polygons and Set Cover · Computing in Geometry and Topology (2024) | TGRS Research Map | TGRS