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.
@InProceedings{dafonseca:LIPIcs.SoCG.2023.67, author = {da Fonseca, Guilherme D.}, title = {{Shadoks Approach to Convex Covering}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {67:1--67:9}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-273-0}, ISSN = {1868-8969}, year = {2023}, volume = {258}, editor = {Chambers, Erin W. and Gudmundsson, Joachim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.67}, URN = {urn:nbn:de:0030-drops-179178}, doi = {10.4230/LIPIcs.SoCG.2023.67}, annote = {Keywords: Set cover, covering, polygons, convexity, heuristics, enumeration, simulated annealing, integer programming, computational geometry} }
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