A polygon C is an intersecting polygon for a set O of objects in ℝ² if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the minimum-area convex intersecting polygon for a given set O of objects. We present an FPTAS for both problems for the case where O is a set of possibly intersecting convex polygons in the plane of total complexity n. Furthermore, we present an exact polynomial-time algorithm for the minimum-perimeter intersecting polygon for the case where O is a set of n possibly intersecting segments in the plane. So far, polynomial-time exact algorithms were only known for the minimum perimeter intersecting polygon of lines or of disjoint segments.
@InProceedings{antoniadis_et_al:LIPIcs.ESA.2022.9, author = {Antoniadis, Antonios and de Berg, Mark and Kisfaludi-Bak, S\'{a}ndor and Skarlatos, Antonis}, title = {{Computing Smallest Convex Intersecting Polygons}}, booktitle = {30th Annual European Symposium on Algorithms (ESA 2022)}, pages = {9:1--9:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-247-1}, ISSN = {1868-8969}, year = {2022}, volume = {244}, editor = {Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.9}, URN = {urn:nbn:de:0030-drops-169470}, doi = {10.4230/LIPIcs.ESA.2022.9}, annote = {Keywords: convex hull, imprecise points, computational geometry} }
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