On Planar Polyline Drawings

  • Huaming Zhang
  • Sadish Sadasivam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)

Abstract

We present a linear time algorithm that produces a planar polyline drawing for a plane graph with n vertices in a grid of size bounded by (p + 1) ×(n − 2), where \(p \leq (\lfloor \frac{2n-5}{3}\rfloor)\). It uses at most \(p \leq \lfloor\frac{2n-5}{3}\rfloor\) bends, and each edge uses at most one bend. Compared with the area optimal polyline drawing algorithm in [3], our algorithm uses a larger grid size bound in trade for a smaller bound on the total number of bends. Their bend bound is (n − 2). Our algorithm is based on a transformation from Schnyder’s realizers [6,7] of maximal plane graphs to transversal structures [4,5] for maximal internally 4-connected plane graphs. This transformation reveals important relations between the two combinatorial structures for plane graphs, which is of independent interest.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Huaming Zhang
    • 1
  • Sadish Sadasivam
    • 1
  1. 1.Computer Science DepartmentUniversity of Alabama in HuntsvilleHuntsvilleUSA

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