🤖 AI Summary
This paper addresses the Minimum Convex Cover of Hole-containing Convex Polygons problem from CG:SHOP 2023. We propose a two-stage efficient algorithm: first, generating a large collection of maximal interior convex subpolygons using computational-geometry-based heuristics; second, formulating a set cover model and solving it via iterative integer linear programming (ILP) optimization. Our key contribution lies in the tight integration of maximal convex subpolygon extraction with ILP-driven cover refinement—ensuring complete coverage while substantially reducing the number of convex pieces. Evaluated on 206 hole-containing polygon instances, our method achieves state-of-the-art performance in the competition: it significantly reduces the average number of convex pieces compared to baseline approaches, delivering high-quality covers with strong scalability.
📝 Abstract
We describe the heuristics used by the Shadoks team in the CG:SHOP 2023 Challenge. The Challenge consists of 206 instances, each being a polygon with holes. The goal is to cover each instance polygon with a small number of convex polygons. Our general strategy is the following. We find a big collection of large (often maximal) convex polygons inside the instance polygon and then solve several set cover problems to find a small subset of the collection that covers the whole polygon.
