Level Planar Embedding in Linear Time

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 u ∈ Vi 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 v ∈ Vi 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 ≤ i ≤ k). We present an O(|V |) time algorithm for embedding level planar graphs. This approach is based on a level planarity test by Junger, Leipert, and Mutzel [6].