Approximating the bottleneck plane perfect matching of a point set

A. Karim Abu-Affash, Ahmad Biniaz, Paz Carmi, Anil Maheshwari, Michiel Smid

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A bottleneck plane perfect matching of a set of n points in ℝ2 is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as bottleneck. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck plane matching of size at least (formula presented.) in O(n log2 n)-time. Then we extend our idea toward an O(n log n)-time approximation algorithm which computes a plane matching of size at least (formula presented.) whose edges have length at most (formula presented.) the bottleneck.

Original languageEnglish
Article number1394
Pages (from-to)718-731
Number of pages14
JournalComputational Geometry: Theory and Applications
Volume48
Issue number9
DOIs
StatePublished - 1 Oct 2015

Keywords

  • Approximation algorithm
  • Bottleneck matching
  • Geometric graph
  • Plane matching
  • Unit disk graph

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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