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Visibility Representations of Four-Connected Plane Graphs with Near Optimal Heights

  • Chieh-Yu Chen
  • Ya-Fei Hung
  • Hsueh-I Lu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)

Abstract

A visibility representation of a graph G is to represent the nodes of G with non-overlapping horizontal line segments such that the line segments representing any two distinct adjacent nodes are vertically visible to each other. If G is a plane graph, i.e., a planar graph equipped with a planar embedding, a visibility representation of G has the additional requirement of reflecting the given planar embedding of G. For the case that G is an n-node four-connected plane graph, we give an O(n)-time algorithm to produce a visibility representation of G with height at most \(\left\lceil\frac{n}{2}\right\rceil+2\left\lceil\sqrt{\frac{n-2}{2}}\right\rceil\). To ensure that the first-order term of the upper bound is optimal, we also show an n-node four-connected plane graph G, for infinite number of n, whose visibility representations require heights at least \(\frac{n}{2}\).

Keywords

Plane Graph Visibility Representation External Boundary Node Label External Node 
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 2009

Authors and Affiliations

  • Chieh-Yu Chen
    • 1
  • Ya-Fei Hung
    • 2
  • Hsueh-I Lu
    • 1
    • 2
  1. 1.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaiwan
  2. 2.Graduate Institute of Networking and MultimediaNational Taiwan UniversityTaipei 106Taiwan, ROC

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