International Symposium on Graph Drawing

GD 1999: Graph Drawing pp 72-81

Level Planar Embedding in Linear Time

  • Michael Jünger
  • Sebastian Leipert
Conference paper

DOI: 10.1007/3-540-46648-7_7

Volume 1731 of the book series Lecture Notes in Computer Science (LNCS)

Abstract

In a level directed acyclic graph G = (V;E) the vertex set V is partitioned into k ≤ |V | levels V1; V2... Vk such that for each edge (u, v) ∈ E with uVi and v ∈; Vj 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 Vi, all vVi are drawn on the line li = {(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 Vi (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].

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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