Lecture Notes in Computer Science Volume 1731, 1999, pp 72-81
Date: 03 Mar 2000

Level Planar Embedding in Linear Time

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Abstract

In a level directed acyclic graph G = (V;E) the vertex set V is partitioned into k ≤ |V | levels V 1; V 2... V k such that for each edge (u, v) ∈ E with uV i and v ∈; V j we have i < j. The level planarity testing problem is to decide if G can be drawn in the plane such that for each level V i, all vV i are drawn on the line l i = {(x, k - i) | x ∈ 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 V i (1 ≤ ik). We present an O(|V |) time algorithm for embedding level planar graphs. This approach is based on a level planarity test by Jünger, Leipert, and Mutzel [6].

Supported by DFG-Grant Ju204/7-3, Forschungsschwerpunkt “Effiziente Algorithmen für diskrete Probleme und ihre Anwendungen”