Upward Planar Drawings of Series-Parallel Digraphs with Maximum Degree Three

An upward planar drawing of a digraph G is a planar drawing of G where every edge is drawn as a simple curve monotone in the vertical direction. A digraph is upward planar if it has an embedding that admits an upward planar drawing. The problem of testing whether a digraph is upward planar is NP-complete. In this paper we give a linear-time algorithm to test the upward planarity of a series-parallel digraph G with maximum degree three and obtain an upward planar drawing of G if G admits one.

[1]  Patrick Healy,et al.  Fixed-Parameter Tractable Algorithms for Testing Upward Planarity , 2005, SOFSEM.

[2]  Carlo Mannino,et al.  Optimal Upward Planarity Testing of Single-Source Digraphs , 1993, ESA.

[3]  Ioannis G. Tollis,et al.  How to Draw a Series-Parallel Digraph , 1994, Int. J. Comput. Geom. Appl..

[4]  Ioannis G. Tollis,et al.  Dynamic Graph Drawings: Trees, Series-Parallel Digraphs, and Planar ST-Digraphs , 1995, SIAM J. Comput..

[5]  Walter Didimo,et al.  Upward Spirality and Upward Planarity Testing , 2005, SIAM J. Discret. Math..

[6]  Roberto Tamassia,et al.  On-Line Planarity Testing , 1989, SIAM J. Comput..

[7]  Roberto Tamassia,et al.  On the Computational Complexity of Upward and Rectilinear Planarity Testing , 1994, SIAM J. Comput..

[8]  Giuseppe Liotta,et al.  Almost Bend-Optimal Planar Orthogonal Drawings of Biconnected Degree-3 Planar Graphs in Quadratic Time , 1999, Graph Drawing.

[9]  Achilleas Papakostas.  Upward Planarity Testing of Outerplanar Dags , 1994, Graph Drawing.

[10]  Carlo Mannino,et al.  Upward drawings of triconnected digraphs , 2005, Algorithmica.

[11]  Robert E. Tarjan,et al.  Efficient Planarity Testing , 1974, JACM.

[12]  R. Tamassia,et al.  Upward planarity testing , 1995 .

[13]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[14]  Kellogg S. Booth,et al.  Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms , 1976, J. Comput. Syst. Sci..

[15]  Carlo Mannino,et al.  Optimal Upward Planarity Testing of Single-Source Digraphs , 1998, SIAM J. Comput..

[16]  Md. Saidur Rahman,et al.  No-bend Orthogonal Drawings of Series-Parallel Graphs , 2005, Graph Drawing.

[17]  Eugene L. Lawler,et al.  The recognition of Series Parallel digraphs , 1979, SIAM J. Comput..