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/
Abrahamsen, Mikkel ;
de Berg, Mark ;
Buchin, Kevin ;
Mehr, Mehran ;
Mehrabi, Ali D.
Minimum Perimeter-Sum Partitions in the Plane
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: |
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Computational geometry, clustering, minimum-perimeter partition, convex hull |
Collection: |
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33rd International Symposium on Computational Geometry (SoCG 2017) |
Issue Date: |
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2017 |
Date of publication: |
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20.06.2017 |