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Fixed-Parameter Algorithms for Computing RAC Drawings of Graphs

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Graph Drawing and Network Visualization (GD 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14466))

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Abstract

In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly \(90^\circ \), where the number of bends on such polylines is typically restricted in some way. While structural and topological properties of RAC drawings have been the focus of extensive research, little was known about the boundaries of tractability for computing such drawings. In this paper, we initiate the study of RAC drawings from the viewpoint of parameterized complexity. In particular, we establish that computing a RAC drawing of an input graph G with at most b bends (or determining that none exists) is fixed-parameter tractable parameterized by either the feedback edge number of G, or b plus the vertex cover number of G.

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Acknowledgments

The authors graciously accept support from the WWTF (Project ICT22-029) and the FWF (Project Y1329) science funds.

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Authors and Affiliations

  1. Algorithms and Complexity Group, TU Wien (Vienna University of Technology), Vienna, Austria

    Cornelius Brand, Robert Ganian, Sebastian Röder & Florian Schager

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  1. Cornelius Brand
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  2. Robert Ganian
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  4. Florian Schager
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Correspondence to Robert Ganian .

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Editors and Affiliations

  1. University of Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. Osnabrück University, Osnabrück, Germany

    Markus Chimani

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Brand, C., Ganian, R., Röder, S., Schager, F. (2023). Fixed-Parameter Algorithms for Computing RAC Drawings of Graphs. In: Bekos, M.A., Chimani, M. (eds) Graph Drawing and Network Visualization. GD 2023. Lecture Notes in Computer Science, vol 14466. Springer, Cham. https://doi.org/10.1007/978-3-031-49275-4_5

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  • DOI: https://doi.org/10.1007/978-3-031-49275-4_5

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