TY - GEN

T1 - Orthogonal drawings of series-parallel graphs with minimum bends

AU - Zhou, Xiao

AU - Nishizeki, Takao

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

AB - 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.

KW - Bend

KW - Orthogonal drawing

KW - Planar graph

KW - Series-parallel graph

UR - http://www.scopus.com/inward/record.url?scp=33744948097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744948097&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33744948097

SN - 3540309357

SN - 9783540309352

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 166

EP - 175

BT - Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings

T2 - 16th International Symposium on Algorithms and Computation, ISAAC 2005

Y2 - 19 December 2005 through 21 December 2005

ER -