2026-07-23T22:07:04Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17319 2024-03-06T10:59:27Z ddc:004 open_access

Minimum Link Fencing Bhore, Sujoy Klute, Fabian Löffler, Maarten Nöllenburg, Martin Terziadis, Soeren Villedieu, Anaïs computational geometry polygon nesting polygon separation We study a variant of the geometric multicut problem, where we are given a set 𝒫 of colored and pairwise interior-disjoint polygons in the plane. The objective is to compute a set of simple closed polygon boundaries (fences) that separate the polygons in such a way that any two polygons that are enclosed by the same fence have the same color, and the total number of links of all fences is minimized. We call this the minimum link fencing (MLF) problem and consider the natural case of bounded minimum link fencing (BMLF), where 𝒫 contains a polygon Q that is unbounded in all directions and can be seen as an outer polygon. We show that BMLF is NP-hard in general and that it is XP-time solvable when each fence contains at most two polygons and the number of segments per fence is the parameter. Finally, we present an O(n log n)-time algorithm for the case that the convex hull of 𝒫⧵{Q} does not intersect Q. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sujoy Bhore and Fabian Klute and Maarten Löffler and Martin Nöllenburg and Soeren Terziadis and Anaïs Villedieu 2022 Is Part Of LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2022.34 urn:nbn:de:0030-drops-173191 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.34 eng https://creativecommons.org/licenses/by/4.0/legalcode