An Optimal Algorithm for Plane Matchings in Multipartite Geometric Graphs

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


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.


Convex Hull General Position Perfect Match Blue Point Colored Match 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ahmad Biniaz
    • 1
    Email author
  • Anil Maheshwari
    • 1
  • Subhas C. Nandy
    • 2
  • Michiel Smid
    • 1
  1. 1.Carleton UniversityOttawaCanada
  2. 2.Indian Statistical InstituteKolkataIndia

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