Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Information Sciences: an International Journal
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Exponential bounds for DPLL below the satisfiability threshold
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
Threshold values of random K-SAT from the cavity method
Random Structures & Algorithms
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
Counting good truth assignments of random k-SAT formulae
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Message-passing and local heuristics as decimation strategies for satisfiability
Proceedings of the 2009 ACM symposium on Applied Computing
A spectral approach to analysing belief propagation for 3-colouring
Combinatorics, Probability and Computing
A Better Algorithm for Random $k$-SAT
SIAM Journal on Computing
Complete convergence of message passing algorithms for some satisfiability problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
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 freezing threshold for k-colourings of a random graph
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Exponential lower bounds for DPLL algorithms on satisfiable random 3-CNF formulas
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Unsatisfiability bounds for random CSPs from an energetic interpolation method
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Going after the k-SAT threshold
Proceedings of the forty-fifth 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
Hi-index | 0.00 |
Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-constructive arguments show that Φ is satisfiable for clause/variable ratios m/n ≤ rk ~ 2k ln 2 with high probability (Achlioptas, Moore: SICOMP 2006; Achlioptas, Peres: J. AMS 2004). Yet no efficient algorithm is know to find a satisfying assignment for densities as low as m/n ~ rk · ln(k)/k with a non-vanishing probability. In fact, the density m/n ~ rk · ln(k)/k seems to form a barrier for a broad class of local search algorithms (Achlioptas, Coja-Oghlan: FOCS 2008). On the basis of deep but non-rigorous statistical mechanics considerations, a message passing algorithm called belief propagation guided decimation for solving random k-SAT has been forward (Mézard, Parisi, Zecchina: Science 2002; Braunstein, Mézard, Zecchina: RSA 2005). Experiments suggest that the algorithm might succeed for densities very close to rk for k = 3, 4, 5 (Kroc, Sabharwal, Selman: SAC 2009). Furnishing the first rigorous analysis of belief propagation guided decimation on random k-SAT, the present paper shows that the algorithm fails to find a satisfying assignment already for m/n ≥ ρ · rk/k, for a constant ρ 0 independent of k.