Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Counting without sampling: new algorithms for enumeration problems using statistical physics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Random sampling of colourings of sparse random graphs with a constant number of colours
Theoretical Computer Science
Computing the density of states of Boolean formulas
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
On belief propagation guided decimation for random k-SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Hi-index | 0.00 |
We present a deterministic approximation algorithm to compute logarithm of the number of 'good' truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by 'good' we mean that violates a small fraction of clauses). The relative error is bounded above by an arbitrarily small constant ε with high probability1 as long as the clause density (ratio of clauses to variables) α u(k) = 2k-1logk(1 + o(1)). The algorithm is based on computation of marginal distribution via belief propagation and use of an interpolation procedure. This scheme substitutes the traditional one based on approximation of marginal probabilities via MCMC, in conjunction with self-reduction, which is not easy to extend to the present problem. Our results are expected hold for a reasonable non-random setup with locally tree-like sparse k-SAT formulas. We derive 2k-1 log k(1+o(1)) as threshold for uniqueness of the Gibbs distribution on satisfying assignment of random infinite tree k-SAT formulae to establish our results, which is of interest in its own right.