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
SN - 0020-0190
VL - 153
JO - Information Processing Letters
JF - Information Processing Letters
M1 - 105860
ER -