Orthogonal drawings of series-parallel graphs with minimum bends

Xiao Zhou, Takao Nishizeki

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

3 Citations (Scopus)


In an orthogonal drawing of a planar graph G, each vertex is drawn as a point, each edge is drawn as a sequence of alternate horizontal and vertical line segments, and any two edges do not cross except at their common end. A bend is a point where an edge changes its direction. A drawing of G is called an optimal orthogonal drawing if the number of bends is minimum among all orthogonal drawings of G. In this paper we give an algorithm to find an optimal orthogonal drawing of any given series-parallel graph of the maximum degree at most three. Our algorithm takes linear time, while the previously known best algorithm takes cubic time. Furthermore, our algorithm is much simpler than the previous one. We also obtain a best possible upper bound on the number of bends in an optimal drawing.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540309357, 9783540309352
Publication statusPublished - 2005
Event16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China
Duration: 2005 Dec 192005 Dec 21

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3827 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other16th International Symposium on Algorithms and Computation, ISAAC 2005


  • Bend
  • Orthogonal drawing
  • Planar graph
  • Series-parallel graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


Dive into the research topics of 'Orthogonal drawings of series-parallel graphs with minimum bends'. Together they form a unique fingerprint.

Cite this