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

Xiao Zhou; Takao Nishizeki

doi:10.1007/978-3-642-10631-6_77

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

Xiao Zhou, Takao Nishizeki

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
Pages	760-770
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-10631-6_77
Publication status	Published - 2009 Dec 1
Event	20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States Duration: 2009 Dec 16 → 2009 Dec 18

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5878 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	20th International Symposium on Algorithms and Computation, ISAAC 2009
Country	United States
City	Honolulu, HI
Period	09/12/16 → 09/12/18

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-642-10631-6_77

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Zhou, X., & Nishizeki, T. (2009). Convex drawings of internally triconnected plane graphs on O(n ²) grids. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings (pp. 760-770). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS). https://doi.org/10.1007/978-3-642-10631-6_77

Convex drawings of internally triconnected plane graphs on O(n ²) grids. / Zhou, Xiao; Nishizeki, Takao.

Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. p. 760-770 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Zhou, X & Nishizeki, T 2009, Convex drawings of internally triconnected plane graphs on O(n ²) grids. in Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5878 LNCS, pp. 760-770, 20th International Symposium on Algorithms and Computation, ISAAC 2009, Honolulu, HI, United States, 09/12/16. https://doi.org/10.1007/978-3-642-10631-6_77

Zhou X, Nishizeki T. Convex drawings of internally triconnected plane graphs on O(n ²) grids. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. p. 760-770. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-10631-6_77

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