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On the solutionspace geometry of random constraint satisfaction problems
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Achlioptas, Dimitris, CojaOghlan, Amin and RicciTersenghi, F. (Federico). (2011) On the solutionspace geometry of random constraint satisfaction problems. Random Structures & Algorithms, Volume 38 (Number 3). pp. 251268. 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 kSAT, 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 kSAT (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: 


Volume:  Volume 38  
Number:  Number 3  
Page Range:  pp. 251268  
Identifier:  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:  CCF0546900 (NSF), 210743 (ERC), CO 646 (DFG)  
References:  [1] D. Achlioptas and A. CojaOghlan, Algorithmic barriers from phase transitions, In Proceedings 
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