# Level Planar Embedding in Linear Time

Jünger, Michael and Leipert, Sebastian (1999) Level Planar Embedding in Linear Time. In: Graph Drawing 7th International Symposium, GD’99, September 15-19, 1999, Štirín Castle, Czech Republic , pp. 72-81 (Official URL: http://dx.doi.org/10.1007/3-540-46648-7_7).

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## Abstract

In a level directed acyclic graph G=(V,E) the vertex set V is partitioned into k \le |V| levels V^1, V^2,..., V^k such that for each edge (u,v) \in E with u \in V^i and v \in 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 \in V^i are drawn on the line l_i={(x,k-i) | x \in R}, the edges are drawn monotonically with respect to the vertical direction, and no edges intersect expect 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 \le i \le 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].

Item Type: Conference Paper 10.1007/3-540-46648-7_7 M Methods > M.500 LayeredG Algorithms and Complexity > G.490 EmbeddingsP Styles > P.480 Layered 273

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