Two-Layer Planarization in Graph Drawing

Abstract. We study the two-layer planarization problems that have applications in Automatic Graph Drawing. We are searching for a two-layer planar subgraph of maximumweight in a given two-layer graph. Depending on the number of layers in which the vertices can be permuted freely, that is, zero, one or two, di erent versions of the problems arise. The latter problem was already investigated in 11] using polyhedral combinatorics. Here, we study the remaining two cases and the relationships between the associated polytopes. In particular, we investigate the polytope P1 associated with the twolayer planarization problem with one xed layer. We provide an overview on the relationships between P1 and the polytope Q1 associated with the two-layer crossing minimization problem with one xed layer, the linear ordering polytope, the two-layer planarization problem with zero and two layers xed. We will see that all facet-de ning inequalities in Q1

• Type: Conference
• Year: 1998
• Where: ISAAC
• Authors: Petra Mutzel, René Weiskircher
• Keywords: Algorithms, ISAAC 1998, Two-layer Graph, Two-layer Planar Subgraph, Two-layer Planarization Problem