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### On the solution-space geometry of random constraint satisfaction problems

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Achlioptas, Dimitris, Coja-Oghlan, Amin and Ricci-Tersenghi, F. (Federico).
(2011)
*On the solution-space geometry of random constraint satisfaction problems.*
Random Structures & Algorithms, Volume 38
(Number 3).
pp. 251-268.
ISSN 10429832

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1002/rsa.20323

## Abstract

For various random constraint satisfaction problems there is a significant gap between the largest constraint density for which solutions exist and the largest density for which any polynomial time algorithm is known to find solutions. Examples of this phenomenon include random k-SAT, random graph coloring, and a number of other random constraint satisfaction problems. To understand this gap, we study the structure of the solution space of random k-SAT (i.e., the set of all satisfying assignments viewed as a subgraph of the Hamming cube). We prove that for densities well below the satisfiability threshold, the solution space decomposes into an exponential number of connected components and give quantitative bounds for the diameter, volume, and number.© 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 251–268, 2011

Item Type: | Journal Article |
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Subjects: | Q Science > QC Physics |

Divisions: | Faculty of Science > Computer Science Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Statistical mechanics, Computational complexity, Constraints (Artificial intelligence) -- Mathematics |

Journal or Publication Title: | Random Structures & Algorithms |

Publisher: | John Wiley & Sons, Inc. |

ISSN: | 10429832 |

Official Date: | May 2011 |

Volume: | Volume 38 |

Number: | Number 3 |

Page Range: | pp. 251-268 |

Identification Number: | 10.1002/rsa.20323 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

Funder: | National Science Foundation (U.S.) (NSF), Alfred P. Sloan Foundation, European Research Council (ERC), Deutsche Forschungsgemeinschaft (DFG) |

Grant number: | CCF-0546900 (NSF), 210743 (ERC), CO 646 (DFG) |

References: | [1] D. Achlioptas and A. Coja-Oghlan, Algorithmic barriers from phase transitions, In Proceedings |

URI: | http://wrap.warwick.ac.uk/id/eprint/41294 |

Data sourced from Thomson Reuters' Web of Knowledge

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