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

Conference paper

DOI: 10.1007/978-3-662-47672-7_31

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)
Cite this paper as:
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

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Institute for Computer Science and ControlHungarian Academy of Sciences (MTA SZTAKI)BudapestHungary

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