WALCOM 2014: Algorithms and Computation pp 337-348

# Bichromatic Point-Set Embeddings of Trees with Fewer Bends

(Extended Abstract)
• Khaled Mahmud Shahriar
• Md. Saidur Rahman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)

## Abstract

Let G be a planar graph such that each vertex of G is colored by either red or blue color. Assume that there are nr red vertices and n b blue vertices in G. Let S be a set of fixed points in the plane such that |S| = n r  + n b where nr points in S are colored by red color and nb points in S are colored by blue color. A bichromatic point-set embedding of G on S is a crossing free drawing of G such that each red vertex of G is mapped to a red point in S, each blue vertex of G is mapped to a blue point in S, and each edge is drawn as a polygonal curve. In this paper, we study the problem of computing bichromatic point-set embeddings of trees on two restricted point-sets which we call “ordered point-set” and “properly-colored point-set”. We show that trees have bichromatic point-set embeddings on these two special types of point-sets with at most one bend per edge and such embeddings can be found in linear time.

## Keywords

Trees Bichromatic point-set embedding Bend Ordered point-set Properly-colored point-set

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© Springer International Publishing Switzerland 2014

## Authors and Affiliations

• Khaled Mahmud Shahriar
• 1
• Md. Saidur Rahman
• 1
1. 1.Department of Computer Science and EngineeringBangladesh University of Engineering and Technology (BUET)DhakaBangladesh