, Volume 68, Issue 4, pp 954-997

2-Layer Right Angle Crossing Drawings

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Abstract

A 2-layer drawing represents a bipartite graph where each vertex is a point on one of two parallel lines, no two vertices on the same line are adjacent, and the edges are straight-line segments. In this paper we study 2-layer drawings where any two crossing edges meet at right angle. We characterize the graphs that admit this type of drawing, provide linear-time testing and embedding algorithms, and present a polynomial-time crossing minimization technique. Also, for a given graph G and a constant k, we prove that it is $\mathcal{NP}$ -complete to decide whether G contains a subgraph of at least k edges having a 2-layer drawing with right angle crossings.

Work supported in part by MIUR of Italy under project AlgoDEEP prot. 2008TFBWL4. An abstract of this work was presented at the International Workshop on Algorithms and Combinatorics (IWOCA 2011) [7].