Small grid drawings of planar graphs with balanced bipartition

Xiao Zhou, Takashi Hikino, Takao Nishizeki

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

3 Citations (Scopus)

Abstract

In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It has been known that every planar graph G of n vertices has a grid drawing on an (n-2)×(n-2) integer grid and such a drawing can be found in linear time. In this paper we show that if a planar graph G has a balanced bipartition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G1 and G2, then G has a grid drawing on a W×H grid such that both the width W and height H are smaller than the larger number of vertices in G1 and in G2. In particular, we show that every series-parallel graph G has a grid drawing on a (2n/3)×(2n/3) grid and such a drawing can be found in linear time.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 4th International Workshop, WALCOM 2010, Proceedings
Pages47-57
Number of pages11
DOIs
Publication statusPublished - 2010 Mar 25
Event4th International Workshop on Algorithms and Computation, WALCOM 2010 - Dhaka, Bangladesh
Duration: 2010 Feb 102010 Feb 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5942 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th International Workshop on Algorithms and Computation, WALCOM 2010
CountryBangladesh
CityDhaka
Period10/2/1010/2/12

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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