A Linear-Time Algorithm for Bend-Optimal Orthogonal Drawings of Biconnected Cubic Plane Graphs

Extended Abstract
  • Shin-ichi Nakano
  • Makiko Yoshikawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)

Abstract

An orthogonal drawing of a plane graph G is a drawing of G with the given planar embedding in which each vertex is mapped to 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. Observe that only a planar graph with the maximum degree four or less has an orthogonal drawing. The best known algorithm to find an orthogonal drawing runs in time O(n7/4√log n) for any plane graph with n vertices. In this paper we give a linear-time algorithm to find an orthogonal drawing of a given biconnected cubic plane graph with the minimum number of bends.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Shin-ichi Nakano
    • 1
  • Makiko Yoshikawa
    • 1
  1. 1.Gunma UniversityKiryuJapan

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