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. (c) 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 251-268, 2011
On the Solution-Space Geometry of Random Constraint Satisfaction Problems / Dimitris, Achlioptas; Coja Oghlan, Amin; RICCI TERSENGHI, Federico. - In: RANDOM STRUCTURES & ALGORITHMS. - ISSN 1042-9832. - 38:3(2011), pp. 251-268. [10.1002/rsa.20323]
On the Solution-Space Geometry of Random Constraint Satisfaction Problems
RICCI TERSENGHI, Federico
2011
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. (c) 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 251-268, 2011I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.