The decimation process in random k-SAT
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The condensation transition in random hypergraph 2-coloring
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The set of solutions of random XORSAT formulae
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The freezing threshold for k-colourings of a random graph
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Limits of local algorithms over sparse random graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
Reconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs
Journal of Combinatorial Optimization
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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 © 2011 Wiley Periodicals, Inc.