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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.

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Notes

  1. A trivial biconnected component consists of a single edge.

  2. Notice that j≤i≤k because z i is in Σ.

  3. In this discussion we consider the case when B i is preceded by a bridge and followed by another bridge. If B i is the first or the last non-trivial biconnected component of skel(G) the situation is analogous, the only difference being that the type of either T(w 1) or T(w 2) is 4 or 5, instead of 2 or 3.

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Acknowledgements

We are very grateful to the anonymous reviewers of this work. Their valuable comments helped us to significantly improve the quality of the paper.

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Authors and Affiliations

  1. Università di Perugia, Perugia, Italy

    Emilio Di Giacomo, Walter Didimo & Giuseppe Liotta

  2. University of Sydney, Sydney, Australia

    Peter Eades

Authors
  1. Emilio Di Giacomo
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  2. Walter Didimo
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  3. Peter Eades
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  4. Giuseppe Liotta
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Corresponding author

Correspondence to Walter Didimo.

Additional information

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].

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Di Giacomo, E., Didimo, W., Eades, P. et al. 2-Layer Right Angle Crossing Drawings. Algorithmica 68, 954–997 (2014). https://doi.org/10.1007/s00453-012-9706-7

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