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Plane 3-trees: Embeddability and Approximation

(Extended Abstract)
  • Stephane Durocher
  • Debajyoti Mondal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

Abstract

We give an O(nlog3 n)-time linear-space algorithm that, given a plane 3-tree G with n vertices and a set S of n points in the plane, determines whether G has a point-set embedding on S (i.e., a planar straight-line drawing of G where each vertex is mapped to a distinct point of S), improving the O(n 4/3 + ε )-time O(n 4/3)-space algorithm of Moosa and Rahman. Given an arbitrary plane graph G and a point set S, Di Giacomo and Liotta gave an algorithm to compute 2-bend point-set embeddings of G on S using O(W 3) area, where W is the length of the longest edge of the bounding box of S. Their algorithm uses O(W 3) area even when the input graphs are restricted to plane 3-trees. We introduce new techniques for computing 2-bend point-set embeddings of plane 3-trees that takes only O(W 2) area. We also give approximation algorithms for point-set embeddings of plane 3-trees. Our results on 2-bend point-set embeddings and approximate point-set embeddings hold for partial plane 3-trees (e.g., series-parallel graphs and Halin graphs).

Keywords

Convex Hull Planar Graph Straight Line Segment Outerplanar Graph Valid Mapping 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stephane Durocher
    • 1
  • Debajyoti Mondal
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaCanada

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