Monochromatic Plane Matchings in Bicolored Point Set

A. Karim Abu-Affash, Sujoy Bhore, Paz Carmi

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations

Abstract

Motivated by networks interplay, we study the problem of computing monochromatic plane matchings in bicolored point set. Given a bicolored set P of n red and m blue points in the plane, where n and m are even, the goal is to compute a plane matching MR of the red points and a plane matching MB of the blue points that minimize the number of crossing between MR and MB as well as the longest edge in MR ∪ MB. In this paper, we give asymptotically tight bound on the number of crossings between MR and MB when the points of P are in convex position. Moreover, we present an algorithm that computes bottleneck plane matchings MR and MB, such that there are no crossings between MR and MB, if such matchings exist. For points in general position, we present a polynomial-time approximation algorithm that computes two plane matchings with linear number of crossings between them.

Original languageEnglish
Pages7-12
Number of pages6
StatePublished - 1 Jan 2017
Event29th Canadian Conference on Computational Geometry, CCCG 2017 - Ottawa, Canada
Duration: 26 Jul 201728 Jul 2017

Conference

Conference29th Canadian Conference on Computational Geometry, CCCG 2017
Country/TerritoryCanada
CityOttawa
Period26/07/1728/07/17

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology

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