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XNLP-Hardness of Parameterized Problems on Planar Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14760))

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Abstract

The class XNLP consists of (parameterized) problems that can be solved nondeterministically in \(f(k)n^{O(1)}\) time and \(g(k)\log n\) space, where n is the size of the input instance and k the parameter. The class XALP consists of problems that can be solved in the above time and space with access to an additional stack. These two classes are a “natural home” for many standard graph problems and their generalizations.

In this paper, we show the hardness of several problems on planar graphs, parameterized by outerplanarity, treewidth and pathwidth, thus strengthening several existing results. In particular, we show XNLP-hardness of the following problems parameterized by outerplanarity: All-or-Nothing Flow, Target Outdegree Orientation, Capacitated (Red-Blue) Dominating Set, Target Set Selection etc. We also show the XNLP-completeness of Scattered Set parameterized by pathwidth and XALP-completeness parameterized by treewidth and outerplanarity.

K. Szilágyi—Supported by the project CRACKNP that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 853234).

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Authors and Affiliations

  1. Utrecht University, Utrecht, The Netherlands

    Hans L. Bodlaender & Krisztina Szilágyi

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  1. Hans L. Bodlaender
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  2. Krisztina Szilágyi
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Correspondence to Krisztina Szilágyi .

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  1. Masaryk University, Brno, Czech Republic

    Daniel Kráľ

  2. University of Primorska, Koper, Slovenia

    Martin Milanič

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Bodlaender, H.L., Szilágyi, K. (2025). XNLP-Hardness of Parameterized Problems on Planar Graphs. In: Kráľ, D., Milanič, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2024. Lecture Notes in Computer Science, vol 14760. Springer, Cham. https://doi.org/10.1007/978-3-031-75409-8_8

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  • DOI: https://doi.org/10.1007/978-3-031-75409-8_8

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