License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2017.4
URN: urn:nbn:de:0030-drops-72048
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7204/
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Abrahamsen, Mikkel ; de Berg, Mark ; Buchin, Kevin ; Mehr, Mehran ; Mehrabi, Ali D.

Minimum Perimeter-Sum Partitions in the Plane

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LIPIcs-SoCG-2017-4.pdf (0.6 MB)

Abstract

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P_1 and P_2 such that the sum of the perimeters of CH(P_1) and CH(P_2) is minimized, where CH(P_i) denotes the convex hull of P_i. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n^2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log^4 n) time and a (1+e)-approximation algorithm running in O(n + 1/e^2 log^4(1/e)) time.

BibTeX - Entry

@InProceedings{abrahamsen_et_al:LIPIcs:2017:7204,
  author =	{Mikkel Abrahamsen and Mark de Berg and Kevin Buchin and Mehran Mehr and Ali D. Mehrabi},
  title =	{{Minimum Perimeter-Sum Partitions in the Plane}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7204},
  URN =		{urn:nbn:de:0030-drops-72048},
  doi =		{10.4230/LIPIcs.SoCG.2017.4},
  annote =	{Keywords: Computational geometry, clustering, minimum-perimeter partition, convex hull}
}

Keywords: Computational geometry, clustering, minimum-perimeter partition, convex hull
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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