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arXiv · 2303.07696

Convex Covering Using Collections of Convex Polygons and Set Cover

Guilherme D. da Fonseca
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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.

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Guilherme D. da Fonseca. 2023-03-14. Convex Covering Using Collections of Convex Polygons and Set Cover. https://doi.org/10.4230/lipics.socg.2023.67

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