# An optimal algorithm for plane matchings in multipartite geometric graphs

## Article Type

Research Article

## Publication Title

Computational Geometry: Theory and Applications

## Abstract

Let P be a set of n points in general position in the plane which is partitioned into color classes. The set P is said to be color-balanced if the number of points of each color is at most ⌊n/2⌋. Given a color-balanced point set P, a balanced cut is a line which partitions P into two color-balanced point sets, each of size at most 2n/3+1. A colored matching of P is a perfect matching in which every edge connects two points of distinct colors by a straight line segment. A plane colored matching is a colored matching which is non-crossing. In this paper, we present an algorithm which computes a balanced cut for P in linear time. Consequently, we present an algorithm which computes a plane colored matching of P optimally in Θ(nlogn) time.

## First Page

1

## Last Page

9

## DOI

10.1016/j.comgeo.2017.02.004

## Publication Date

6-1-2017

## Recommended Citation

Biniaz, Ahmad; Maheshwari, Anil; Nandy, Subhas C.; and Smid, Michiel, "An optimal algorithm for plane matchings in multipartite geometric graphs" (2017). *Journal Articles*. 2555.

https://digitalcommons.isical.ac.in/journal-articles/2555

## Comments

Open Access, Bronze