Orthogonal drawings of series-parallel graphs with minimum bends

Xiao Zhou, Takao Nishizekl

Research output: Contribution to journalArticlepeer-review

18 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
Pages (from-to)1570-1604
Number of pages35
JournalSIAM Journal on Discrete Mathematics
Issue number4
Publication statusPublished - 2008


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


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