Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Tail bounds for occupancy and the satisfiability threshold conjecture
Random Structures & Algorithms
A general upper bound for the satisfiability threshold of random r-SAT formulae
Journal of Algorithms
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
The Asymptotic Order of the Random k -SAT Threshold
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Linear Upper Bounds for Random Walk on Small Density Random 3-CNF
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A new look at survey propagation and its generalizations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The generalized distributive law
IEEE Transactions on Information Theory
A new look at survey propagation and its generalizations
Journal of the ACM (JACM)
Pairs of SAT-assignments in random Boolean formulæ
Theoretical Computer Science
On the satisfiability threshold and clustering of solutions of random 3-SAT formulas
Theoretical Computer Science
On the satisfiability threshold of formulas with three literals per clause
Theoretical Computer Science
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
On the random satisfiable process
Combinatorics, Probability and Computing
On the boolean connectivity problem for horn relations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
Does more connectivity help groups to solve social problems
Proceedings of the 12th ACM conference on Electronic commerce
Discrete Applied Mathematics
Some results on average-case hardness within the polynomial hierarchy
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
The condensation transition in random hypergraph 2-coloring
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The connectivity of boolean satisfiability: computational and structural dichotomies
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Uniquely satisfiable k-SAT instances with almost minimal occurrences of each variable
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Catching the k-NAESAT threshold
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The freezing threshold for k-colourings of a random graph
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
For a number of random constraint satisfaction problems, such as random k-SAT and random graph/hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known polynomial-time algorithms for these problems fail to find solutions even at much lower densities. To understand the origin of this gap we study how the structure of the space of solutions evolves in such problems as constraints are added. In particular, we prove that much before solutions disappear, they organize into an exponential number of clusters, each of which is relatively small and far apart from all other clusters. Moreover, inside each cluster most variables are frozen, i.e., take only one value. The existence of such frozen variables gives a satisfying intuitive explanation for the failure of the polynomial-time algorithms analyzed so far. At the same time, our results establish rigorously one of the two main hypotheses underlying Survey Propagation, a heuristic introduced by physicists in recent years that appears to perform extraordinarily well on random constraint satisfaction problems.