2012 IEEE 27th Conference on Computational Complexity (2012)

Porto Portugal

June 26, 2012 to June 29, 2012

ISSN: 1093-0159

ISBN: 978-0-7695-4708-4

pp: 74-84

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2012.36

ABSTRACT

The field of exact exponential time algorithms for NP-hard problems has thrived over the last decade. While exhaustive search remains asymptotically the fastest known algorithm for some basic problems, difficult and non-trivial exponential time algorithms have been found for a myriad of problems, including Graph Coloring, Hamiltonian Path, Dominating Set and 3-CNF-Sat. In some instances, improving these algorithms further seems to be out of reach. The CNF-Sat problem is the canonical example of a problem for which the trivial exhaustive search algorithm runs in time O(2^n), where n is the number of variables in the input formula. While there exist non-trivial algorithms for CNF-Sat that run in time o(2^n), no algorithm was able to improve the growth rate 2 to a smaller constant, and hence it is natural to conjecture that 2 is the optimal growth rate. The strong exponential time hypothesis (SETH) by Impagliazzo and Paturi [JCSS 2001] goes a little bit further and asserts that, for every epsilon

INDEX TERMS

Sparsification Lemma, Strong Exponential Time Hypothesis, Exponential Time Algorithms

CITATION

"On Problems as Hard as CNF-SAT,"

*2012 IEEE 27th Conference on Computational Complexity(CCC)*, Porto Portugal, 2012, pp. 74-84.

doi:10.1109/CCC.2012.36