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Parameterized and Approximation Algorithms for the Maximum Bimodal Subgraph Problem

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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

A vertex of a plane digraph is bimodal if all its incoming edges (and hence all its outgoing edges) are consecutive in the cyclic order around it. A plane digraph is bimodal if all its vertices are bimodal. Bimodality is at the heart of many types of graph layouts, such as upward drawings, level-planar drawings, and L-drawings. If the graph is not bimodal, the Maximum Bimodal Subgraph (MBS) problem asks for an embedding-preserving bimodal subgraph with the maximum number of edges. We initiate the study of the MBS problem from the parameterized complexity perspective with two main results: (i) we describe an FPT algorithm parameterized by the branchwidth (and hence by the treewidth) of the graph; (ii) we establish that MBS parameterized by the number of non-bimodal vertices admits a polynomial kernel. As the byproduct of these results, we obtain a subexponential FPT algorithm and an efficient polynomial-time approximation scheme for MBS.

Research started at the Dagstuhl Seminar 23162: New Frontiers of Parameterized Complexity in Graph Drawing, April 2023, and partially supported by: (i) University of Perugia, Ricerca Base 2021, Proj. “AIDMIX - Artificial Intelligence for Decision Making: Methods for Interpretability and eXplainability”; (ii) MUR PRIN Proj. 2022TS4Y3N - “EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data”, (iii) MUR PRIN Proj. 2022ME9Z78 - “NextGRAAL: Next-generation algorithms for constrained GRAph visuALization”, (iv) the Research Council of Norway project BWCA 314528, (v) the European Research Council (ERC) grant LOPPRE 819416, and (vi) NSF-CCF 2212130.

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Authors and Affiliations

  1. Department of Engineering, University of Perugia, Perugia, Italy

    Walter Didimo

  2. Department of Computer Science, University of Bergen, Bergen, Norway

    Fedor V. Fomin, Petr A. Golovach & Tanmay Inamdar

  3. Department of Computer Science, University of Arizona, Tucson, USA

    Stephen Kobourov

  4. Department of Computer Science, University of Würzburg, Würzburg, Germany

    Marie Diana Sieper

Authors
  1. Walter Didimo
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  2. Fedor V. Fomin
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  3. Petr A. Golovach
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  4. Tanmay Inamdar
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  5. Stephen Kobourov
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  6. Marie Diana Sieper
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Correspondence to Marie Diana Sieper .

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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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Didimo, W., Fomin, F.V., Golovach, P.A., Inamdar, T., Kobourov, S., Sieper, M.D. (2023). Parameterized and Approximation Algorithms for the Maximum Bimodal Subgraph Problem. 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_13

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  • DOI: https://doi.org/10.1007/978-3-031-49275-4_13

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  • Online ISBN: 978-3-031-49275-4

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