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Directed Ear Anonymity

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LATIN 2024: Theoretical Informatics (LATIN 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14579))

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Abstract

We define and study a new structural parameter for directed graphs, which we call ear anonymity. Our parameter aims to generalize the useful properties of funnels to larger digraph classes. In particular, funnels are exactly the acyclic digraphs with ear anonymity one. We prove that computing the ear anonymity of a digraph is NP-hard and that it can be solved in \(\mathcal {O}(m(n + m))\)-time on acyclic digraphs (where \(n\) is the number of vertices and \(m\) is the number of arcs in the input digraph). It remains open where exactly in the polynomial hierarchy the problem of computing ear anonymity lies, however for a related problem we manage to show \(\varSigma _2^p\)-completeness.

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Notes

  1. 1.

    Maximal with respect to the subgraph relation.

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Acknowledgments

An anonymous reviewer provided useful insights which helped improve the running time of the algorithms in Lemma 4 and Theorems 1 and 2.

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Marcelo Garlet Milani

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  1. Marcelo Garlet Milani
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Correspondence to Marcelo Garlet Milani .

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Editors and Affiliations

  1. DIM-CMM, Universidad de Chile, Santiago, Chile

    José A. Soto

  2. Technical University of Munich, Munich, Germany

    Andreas Wiese

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Milani, M.G. (2024). Directed Ear Anonymity. In: Soto, J.A., Wiese, A. (eds) LATIN 2024: Theoretical Informatics. LATIN 2024. Lecture Notes in Computer Science, vol 14579. Springer, Cham. https://doi.org/10.1007/978-3-031-55601-2_6

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  • DOI: https://doi.org/10.1007/978-3-031-55601-2_6

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  • Print ISBN: 978-3-031-55600-5

  • Online ISBN: 978-3-031-55601-2

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