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Computing Tree-Depth Faster Than \(2^{n}\)

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Abstract

A connected graph has tree-depth at most \(k\) if it is a subgraph of the closure of a rooted tree whose height is at most \(k\). We give an algorithm which for a given \(n\)-vertex graph \(G\), in time \({\mathcal {O}^*}(1.9602^n)\) computes the tree-depth of \(G\). Our algorithm is based on combinatorial results revealing the structure of minimal rooted trees whose closures contain \(G\).

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Notes

  1. The \({\mathcal {O}^*}(\cdot )\) notation suppresses factors that are polynomial in the input size.

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Acknowledgments

Supported by European Research Council (ERC) Grant ”Rigorous Theory of Preprocessing”, reference 267959

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, P.O. Box 7803, 5020  , Bergen, Norway

    Fedor V. Fomin, Archontia C. Giannopoulou & Michał Pilipczuk

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  1. Fedor V. Fomin
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  2. Archontia C. Giannopoulou
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  3. Michał Pilipczuk
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Correspondence to Archontia C. Giannopoulou.

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Fomin, F.V., Giannopoulou, A.C. & Pilipczuk, M. Computing Tree-Depth Faster Than \(2^{n}\) . Algorithmica 73, 202–216 (2015). https://doi.org/10.1007/s00453-014-9914-4

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