TY - JOUR

T1 - Monochromatic Plane Matchings in Bicolored Point Set

AU - Karim Abu-Affash, A.

AU - Bhore, Sujoy

AU - Carmi, Paz

N1 - Funding Information:
Work by A.K. Abu-Affash was partially supported by Grant 2016116 from the United States-Israel Binational Science Foundation.Work by S. Bhore was partially supported by the Lynn and William Frankel Center for Computer Science.Work by P. Carmi was partially supported by the Lynn and William Frankel Center for Computer Science and by Grant 2016116 from the United States-Israel Binational Science Foundation.
Publisher Copyright:
© 2019 Elsevier B.V.

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

UR - http://www.scopus.com/inward/record.url?scp=85073924094&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2019.105860

DO - 10.1016/j.ipl.2019.105860

M3 - Article

AN - SCOPUS:85073924094

VL - 153

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

M1 - 105860

ER -