Convex drawings of internally triconnected plane graphs on O(n 2) grids

Xiao Zhou, Takao Nishizeki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In a convex grid drawing of a plane graph, every edge is drawn as a straight-line segment without any edge-intersection, every vertex is located at a grid point, and every facial cycle is drawn as a convex polygon. A plane graph G has a convex drawing if and only if G is internally triconnected. It has been known that an internally triconnected plane graph G of n vertices has a convex grid drawing on a grid of O(n 3) area if the triconnected component decomposition tree of G has at most four leaves. In this paper, we improve the area bound O(n 3) to O(n 2), which is optimal up to a constant factor. More precisely, we show that G has a convex grid drawing on a 2n×4n grid. We also present an algorithm to find such a drawing in linear time.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
Pages760-770
Number of pages11
DOIs
Publication statusPublished - 2009 Dec 1
Event20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States
Duration: 2009 Dec 162009 Dec 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5878 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other20th International Symposium on Algorithms and Computation, ISAAC 2009
CountryUnited States
CityHonolulu, HI
Period09/12/1609/12/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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