Upward Planar Drawings of Series-Parallel Digraphs with Maximum Degree Three
نویسندگان
چکیده
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.
منابع مشابه
1-Bend Upward Planar Drawings of SP-Digraphs
It is proved that every series-parallel digraph whose maximum vertex-degree is ∆ admits an upward planar drawing with at most one bend per edge such that each edge segment has one of ∆ distinct slopes. This is shown to be worst-case optimal in terms of the number of slopes. Furthermore, our construction gives rise to drawings with optimal angular resolution π ∆ . A variant of the proof techniqu...
متن کاملLinkless symmetric drawings of series parallel digraphs
In this paper, we present a linear time algorithm for constructing linkless drawings of series parallel digraphs with maximum number of symmetries. Linkless drawing in three dimensions is a natural extension to planar drawing in two dimensions. Symmetry is one of the most important aesthetic criteria in graph drawing. More specifically, we present two algorithms: a symmetry finding algorithm wh...
متن کاملDrawing series parallel digraphs symmetrically
In this paper we present algorithms for drawing series parallel digraphs with as much symmetry as possible. The first step is to compute a certain kind of automorphism, called an “upward planar automorphism” for an input series parallel digraph. The next step uses these automorphisms to construct a symmetric drawing of the graph. We present several variations of the second step, with visibility...
متن کاملUniversal Slope Sets for Upward Planar Drawings
We prove that every set S of ∆ slopes containing the horizontal slope is universal for 1-bend upward planar drawings of bitonic st-graphs with maximum vertex degree ∆, i.e., every such digraph admits a 1-bend upward planar drawing whose edge segments use only slopes in S. This result is worst-case optimal in terms of the number of slopes, and, for a suitable choice of S, it gives rise to drawin...
متن کاملCapturing Lombardi Flow in Orthogonal Drawings by Minimizing the Number of Segments
Inspired by the artwork of Mark Lombardi, we study the problem of constructing orthogonal drawings where a small number of horizontal and vertical line segments covers all vertices. We study two problems on orthogonal drawings of planar graphs, one that minimizes the total number of line segments and another that minimizes the number of line segments that cover all the vertices. We show that th...
متن کامل