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Block Interpolation: A Framework for Tight Exponential-Time Counting Complexity

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9134))

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Abstract

We devise a framework for proving tight lower bounds under the counting exponential-time hypothesis \(\mathsf {\#ETH}\) introduced by Dell et al. Our framework allows to convert many known \(\mathsf {\#P}\)-hardness results for counting problems into results of the following type: If the given problem admits an algorithm with running time \(2^{o(n)}\) on graphs with \(n\) vertices and \(\mathcal {O}(n)\) edges, then \(\mathsf {\#ETH}\) fails. As exemplary applications of this framework, we obtain such tight lower bounds for the evaluation of the zero-one permanent, the matching polynomial, and the Tutte polynomial on all non-easy points except for two lines.

R. Curticapean—Supported by ERC Starting Grant PARAMTIGHT (No. 280152).

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Authors and Affiliations

  1. Department of Computer Science, Saarland University, Saarbrücken, Germany

    Radu Curticapean

  2. Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Budapest, Hungary

    Radu Curticapean

Authors
  1. Radu Curticapean
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Correspondence to Radu Curticapean .

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Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Curticapean, R. (2015). Block Interpolation: A Framework for Tight Exponential-Time Counting Complexity. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_31

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  • DOI: https://doi.org/10.1007/978-3-662-47672-7_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47671-0

  • Online ISBN: 978-3-662-47672-7

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