Monochromatic plane matchings in bicolored point set

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

doi:10.1016/j.ipl.2019.105860

Monochromatic plane matchings in bicolored point set

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

Research output: Contribution to journal › Article › peer-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 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 length of 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	English
Article number	105860
Journal	Information Processing Letters
Volume	153
DOIs	https://doi.org/10.1016/j.ipl.2019.105860
State	Published - 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

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10.1016/j.ipl.2019.105860

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 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.",

keywords = "Approximation algorithms, Bicolored point sets, Bottleneck matching, Plane matching",

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T1 - Monochromatic plane matchings in bicolored point set

AU - Karim Abu-Affash, A.

AU - Bhore, Sujoy

AU - Carmi, Paz

PY - 2020/1/1

Y1 - 2020/1/1

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 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.

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 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.

KW - Approximation algorithms

KW - Bicolored point sets

KW - Bottleneck matching

KW - Plane matching

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DO - 10.1016/j.ipl.2019.105860

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Monochromatic plane matchings in bicolored point set

Abstract

Keywords

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