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On the Intractability Landscape of Digraph Intersection Representations

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Combinatorial Algorithms (IWOCA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13270))

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Abstract

We study the classical graph intersection number problem [Erdős et al., CJM1966] for directed acyclic graphs as recently proposed in [Kostochka et al., ISIT2019]. We prove a strong inapproximability result for arbitrary DAGs. We show that the problem is NP-hard when restricted to arborescences, which strongly contrasts with the existence of a trivial linear time solution for the corresponding problem on undirected trees. For the restriction of the problem to the case of arborescences, we complement the hardness result with an asymptotic FPTAS, which significantly improves on a previously known 2-approximation algorithm.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Andrea Caucchiolo & Ferdinando Cicalese

Authors
  1. Andrea Caucchiolo
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  2. Ferdinando Cicalese
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Correspondence to Ferdinando Cicalese .

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Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Cristina Bazgan

  2. Universität Trier, Trier, Germany

    Henning Fernau

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Caucchiolo, A., Cicalese, F. (2022). On the Intractability Landscape of Digraph Intersection Representations. In: Bazgan, C., Fernau, H. (eds) Combinatorial Algorithms. IWOCA 2022. Lecture Notes in Computer Science, vol 13270. Springer, Cham. https://doi.org/10.1007/978-3-031-06678-8_20

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  • DOI: https://doi.org/10.1007/978-3-031-06678-8_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06677-1

  • Online ISBN: 978-3-031-06678-8

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