Minimum perimeter-sum partitions in the plane

Mikkel Abrahamsen; Mark de Berg; Kevin Buchin; Mehran Mehr; Ali D. Mehrabi

doi:10.4230/LIPIcs.SoCG.2017.4

Minimum perimeter-sum partitions in the plane

Mikkel Abrahamsen, Mark de Berg, Kevin Buchin, Mehran Mehr, Ali D. Mehrabi

Department of Computer Science

3 Citations (Scopus)

39 Downloads (Pure)

Abstract

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P₁ and P₂ such that the sum of the perimeters of CH(P₁) and CH(P₂) 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(n²) 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 log⁴ n) time and a (1 + ϵ)-approximation algorithm running in O(n + 1/ϵ² · log⁴ (1/ϵ)) time.

Original language	English
Title of host publication	33rd International Symposium on Computational Geometry (SoCG 2017)
Editors	Boris Aronov, Matthew J. Katz
Number of pages	15
Publisher	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication date	2017
Article number	4
ISBN (Electronic)	978-3-95977-038-5
DOIs	https://doi.org/10.4230/LIPIcs.SoCG.2017.4
Publication status	Published - 2017
Event	33rd International Symposium on Computational Geometry - Brisbane, Australia Duration: 4 Jul 2017 → 7 Jul 2017 Conference number: 33

Conference

Conference	33rd International Symposium on Computational Geometry
Number	33
Country/Territory	Australia
City	Brisbane
Period	04/07/2017 → 07/07/2017

Series	Leibniz International Proceedings in Informatics
Volume	77
ISSN	1868-8969

Keywords

Clustering
Computational geometry
Convex hull
Minimum-perimeter partition

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Abrahamsen_2017_Minimum_perimeter-sumFinal published version, 652 KBLicence: CC BY

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Abrahamsen, M., de Berg, M., Buchin, K., Mehr, M., & Mehrabi, A. D. (2017). Minimum perimeter-sum partitions in the plane. In B. Aronov, & M. J. Katz (Eds.), 33rd International Symposium on Computational Geometry (SoCG 2017) [4] Schloss Dagstuhl - Leibniz-Zentrum für Informatik. Leibniz International Proceedings in Informatics Vol. 77 https://doi.org/10.4230/LIPIcs.SoCG.2017.4

Minimum perimeter-sum partitions in the plane. / Abrahamsen, Mikkel; de Berg, Mark; Buchin, Kevin et al.

33rd International Symposium on Computational Geometry (SoCG 2017). ed. / Boris Aronov; Matthew J. Katz. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. 4 (Leibniz International Proceedings in Informatics, Vol. 77).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abrahamsen, M, de Berg, M, Buchin, K, Mehr, M & Mehrabi, AD 2017, Minimum perimeter-sum partitions in the plane. in B Aronov & MJ Katz (eds), 33rd International Symposium on Computational Geometry (SoCG 2017)., 4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Leibniz International Proceedings in Informatics, vol. 77, 33rd International Symposium on Computational Geometry, Brisbane, Queensland, Australia, 04/07/2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.4

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Minimum perimeter-sum partitions in the plane

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