Monochromatic plane matchings in bicolored point set

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

Monochromatic plane matchings in bicolored point set

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

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Contribution to conference › Paper › peer-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 M_R of the red points and a plane matching M_B of the blue points that minimize the number of crossing between M_R and M_B as well as the longest edge in M_R ∪ M_B. In this paper, we give asymptotically tight bound on the number of crossings between M_R and M_B when the points of P are in convex position. Moreover, we present an algorithm that computes bottleneck plane matchings M_R and M_B, such that there are no crossings between M_R and M_B, 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 language	American English
Pages	7-12
Number of pages	6
State	Published - 1 Jan 2017
Event	29th Canadian Conference on Computational Geometry, CCCG 2017 - Ottawa, Canada Duration: 26 Jul 2017 → 28 Jul 2017

Conference

Conference	29th Canadian Conference on Computational Geometry, CCCG 2017
Country/Territory	Canada
City	Ottawa
Period	26/07/17 → 28/07/17

All Science Journal Classification (ASJC) codes

Computational Mathematics
Geometry and Topology

Cite this

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title = "Monochromatic plane matchings in bicolored point set",

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.",

author = "{Karim Abu-Affash}, A. and Sujoy Bhore and Paz Carmi",

note = "Publisher Copyright: Compilation copyright {\textcopyright} 2017 Michiel Smid Copyright of individual papers retained by authors.All right reserved.; 29th Canadian Conference on Computational Geometry, CCCG 2017 ; Conference date: 26-07-2017 Through 28-07-2017",

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AU - Karim Abu-Affash, A.

AU - Bhore, Sujoy

AU - Carmi, Paz

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N2 - 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.

AB - 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.

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M3 - Paper

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T2 - 29th Canadian Conference on Computational Geometry, CCCG 2017

Y2 - 26 July 2017 through 28 July 2017

ER -

Monochromatic plane matchings in bicolored point set

Abstract

Conference

All Science Journal Classification (ASJC) codes

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