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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

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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

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

Dates:

Date	Event
May 2011	Published

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)

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