Bottleneck non-crossing matching in the plane

A. Karim Abu-Affash, Paz Carmi, Matthew J. Katz, Yohai Trabelsi

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Let P be a set of 2n points in the plane, and let MC (resp., MNC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing MNC. We first prove that the problem is NP-hard and does not admit a PTAS. Then, we present an O(n1.5log0.5n)-time algorithm that computes a non-crossing matching M of P, such that bn(M)≤210×bn(MNC), where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(MNC)/bn(MC)≤210. Finally, we show that when the points of P are in convex position, one can compute MNC in O(n3) time, improving a result in [7].

Original languageEnglish
Pages (from-to)447-457
Number of pages11
JournalComputational Geometry: Theory and Applications
Volume47
Issue number3 PART A
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Approximation algorithms
  • Bottleneck matching
  • NP-hardness
  • Non-crossing configuration

ASJC Scopus subject areas

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

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