Shadoks Approach to Convex Covering (CG Challenge)

Author Guilherme D. da Fonseca

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Guilherme D. da Fonseca
  • LIS, Aix-Marseille Université, France


We would like to thank the Challenge organizers and other competitors for their time, feedback, and making this whole event possible. We would also like to thank the second year undergraduate students Rayis Berkat, Ian Bertin, Ulysse Holzinger, and Julien Jamme for coding a solution visualisation tool that allows you to view all our best solutions in

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Guilherme D. da Fonseca. Shadoks Approach to Convex Covering (CG Challenge). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 67:1-67:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Set cover
  • covering
  • polygons
  • convexity
  • heuristics
  • enumeration
  • simulated annealing
  • integer programming
  • computational geometry


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