License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.34
URN: urn:nbn:de:0030-drops-173191
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17319/
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Bhore, Sujoy ; Klute, Fabian ; Löffler, Maarten ; Nöllenburg, Martin ; Terziadis, Soeren ; Villedieu, Anaïs

Minimum Link Fencing

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LIPIcs-ISAAC-2022-34.pdf (1 MB)

Abstract

We study a variant of the geometric multicut problem, where we are given a set ? 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 ? 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 ?⧵{Q} does not intersect Q.

BibTeX - Entry

@InProceedings{bhore_et_al:LIPIcs.ISAAC.2022.34,
  author =	{Bhore, Sujoy and Klute, Fabian and L\"{o}ffler, Maarten and N\"{o}llenburg, Martin and Terziadis, Soeren and Villedieu, Ana\"{i}s},
  title =	{{Minimum Link Fencing}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{34:1--34:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17319},
  URN =		{urn:nbn:de:0030-drops-173191},
  doi =		{10.4230/LIPIcs.ISAAC.2022.34},
  annote =	{Keywords: computational geometry, polygon nesting, polygon separation}
}

Keywords: computational geometry, polygon nesting, polygon separation
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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