Monochromatic Plane Matchings in Bicolored Point Set

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

Research output: Contribution to journalArticlepeer-review

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 length of 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
Article number105860
JournalInformation Processing Letters
Volume153
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Approximation algorithms
  • Bicolored point sets
  • Bottleneck matching
  • Plane matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Monochromatic Plane Matchings in Bicolored Point Set'. Together they form a unique fingerprint.

Cite this