Bottleneck non-crossing matching in the plane

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Let P be a set of 2n points in the plane, and let M C (resp., M NC) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of P. We study the problem of computing M NC. We present an O(n 1.5log 0.5 n)-time algorithm that computes a non-crossing matching M of P, such that bn(M) ≤ 2√10·bnM NC, where bn(M) is the length of a longest edge in M. An interesting implication of our construction is that bn(M NC)/bn(M NC) ≤ 22√10. We also show that when the points of P are in convex position, one can compute M NC in O(n 3) time. (In the full version of this paper, we also prove that the problem is NP-hard and does not admit a PTAS.)

Original languageEnglish
Title of host publicationAlgorithms, ESA 2012 - 20th Annual European Symposium, Proceedings
Number of pages12
StatePublished - 1 Oct 2012
Event20th Annual European Symposium on Algorithms, ESA 2012 - Ljubljana, Slovenia
Duration: 10 Sep 201212 Sep 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7501 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th Annual European Symposium on Algorithms, ESA 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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