Minimum perimeter-sum partitions in the plane

Mikkel Abrahamsen (Corresponding author), Mark de Berg, Kevin Buchin, Mehran Mehr, Ali D. Mehrabi

Research output: Contribution to journalArticleAcademicpeer-review

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(Pi) denotes the convex hull of Pi. 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(nlog 2n) time and a (1 + ε) -approximation algorithm running in O(n+ 1 / ε2· log 2(1 / ε)) time.

Original languageEnglish
Pages (from-to)483-505
Number of pages23
JournalDiscrete and Computational Geometry
Volume63
Issue number2
Early online date1 Jan 2019
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • Clustering
  • Computational geometry
  • Convex hull
  • Minimum-perimeter partition

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