WADS 2015: Algorithms and Data Structures pp 66-78

# An Optimal Algorithm for Plane Matchings in Multipartite Geometric Graphs

• Anil Maheshwari
• Subhas C. Nandy
• Michiel Smid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)

## Abstract

Let P be a set of n points in general position in the plane which is partitioned into color classes. P is said to be color-balanced if the number of points of each color is at most $$\lfloor n/2\rfloor$$. 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 $$\Theta (n\log n)$$ time.

## Keywords

Convex Hull General Position Perfect Match Blue Point Colored Match
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• 1
Email author
• Anil Maheshwari
• 1
• Subhas C. Nandy
• 2
• Michiel Smid
• 1