Jünger, Michael and Leipert, Sebastian
(2002)
Level Planar Embedding in linear Time.
[Journal (Online/Unpaginated)]
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Abstract
A level graph G = (V,E,lev) is a directed acyclic graph with a mapping lev : V > {1,2,dots,k}, k >= 1, that partitions the vertex set V as V = V1 u V2 u...u Vk, Vj = lev^{1}(j), Vi n Vj = 0 for i != j, such that lev(v) >= lev(u) + 1 for each edge (u,v) in E. The level planarity testing problem is to decide if G can be drawn in the plane such that for each level Vi, all v in Vi are drawn on the line l_i = {(x,ki)  x in R}, the edges are drawn monotonically with respect to the vertical direction, and no edges intersect except at their end vertices.
In order to draw a level planar graph without edge crossings, a level planar embedding of the level graph has to be computed. Level planar embeddings are characterized by linear orderings of the vertices in each Vi (1 <= i <= k). We present an order(V) time algorithm for embedding level planar graphs. This approach is based on a level planarity test by Jünger, Leipert, Mutzel 1999.
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