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 u ∈ V 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 v ∈ V 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 ≤ i ≤ k). 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”
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© 1999 Springer-Verlag Berlin Heidelberg
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Jünger, M., Leipert, S. (1999). Level Planar Embedding in Linear Time. In: Kratochvíyl, J. (eds) Graph Drawing. GD 1999. Lecture Notes in Computer Science, vol 1731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46648-7_7
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DOI: https://doi.org/10.1007/3-540-46648-7_7
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