# On problems as hard as CNF-SAT

Cygan, M and Dell, H and Lokshtanov, D and Marx, Dániel and Nederlof, J and Okamoto, Y and Paturi, R and Saurabh, S and Wahlström, M
(2012)
*On problems as hard as CNF-SAT.*
In: 2012 IEEE 27th Annual Conference on Computational Complexity, 2012-06-26 - 2012-06-29, Porto, Portugália.
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 © 2012 IEEE.

Item Type: | Conference or Workshop Item (-) |
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Additional Information: | #Könyv Szerző ismeretlen |

Uncontrolled Keywords: | Algorithms, Computational complexity, sparsification, Optimal growth, Non-trivial algorithms, Non-trivial, Hamiltonian path, Graph colorings, Exponential time hypothesis, Exponential time algorithm, Exhaustive search algorithms, Exhaustive search, Dominating sets, Strong Exponential Time Hypothesis, Sparsification Lemma, Exponential Time Algorithms |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Depositing User: | EPrints Admin |

Date Deposited: | 16 Jan 2014 10:30 |

Last Modified: | 05 Feb 2014 12:27 |

URI: | https://eprints.sztaki.hu/id/eprint/7336 |

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