Orthogonal drawings of series-parallel graphs with minimum bends

Authors:
Xiao Zhou;Takao Nishizeki
Affiliations:
Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

Citing 11
Cited 1

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On the Computational Complexity of Upward and Rectilinear Planarity Testing

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On the two-dimensional orthogonal drawing of series-parallel graphs

Discrete Applied Mathematics

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Abstract

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.