Level Planar Embedding in Linear Time

  • Michael Jünger
  • Sebastian Leipert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)


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].


Linear Time Level Versus Outgoing Edge Incoming Edge Level Planar 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Michael Jünger
    • 1
  • Sebastian Leipert
    • 1
  1. 1.Universität zu KölnInstitut für InformatikKölnGermany

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