Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k = 3, 4, 5, 6.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k = 3, 4, 5, 6.

With such a representation, we can design branching strategies by inferring the marginal probabilities of each variable assignment.

With such a representation, we can design branching strategies by inferring the marginal probabilities of each variable assignment.

Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common deriva- tion of survey propagation, belief propagation and several interesting hy- brid methods. We then present numerical experiments which use WSAT (a widely used random-walk based SAT solver) to quantify the complex- ity of the 3-SAT formulae as a function of their parameters, both as ran- domly generated and after simplication, guided by survey propagation. Some properties of WSAT which have not previously been reported make it an ideal tool for this purpose its mean cost is proportional to the num- ber of variables in the formula (at a xed ratio of clauses to variables) in the easy-SAT regime and slightly beyond, and its behavior in the hard- SAT regime appears to reect the underlying structure of the solution space that has been predicted by replica symmetry-breaking arguments. An analysis of the tradeoffs between the various methods of search for satisfying assignments shows WSAT to be far more powerful than has been appreciated, and suggests some interesting new directions for prac- tical algorithm development.

Many natural optimization problems are NP-hard, which implies that they are probably hard to solve exactly in the worst-case. However, in practice, it suffices to get reasonably good solutions for all (or even most) instances. This paper presents a new algorithm for computing approximate solution in ${\Theta(N})$ for the MAX-E-$3$-SAT problem by using deep learning methodology. This methodology allows us to create a learning algorithm able to fix Boolean variables by using local information obtained by the Survey Propagation algorithm. By performing an accurate analysis, on random CNF instances of the MAX-E-$3$-SAT with several Boolean variables, we show that this new algorithm, avoiding any decimation strategy, can build assignments better than a random one, even if the convergence of the messages is not found. Although this algorithm is not competitive with state-of-the-art MAX-SAT solvers, it can solve substantially larger and more difficult problems than it ever saw during training.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k 3, 4, 5, 6. Papers published at the Neural Information Processing Systems Conference.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k = 3, 4, 5, 6.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k = 3, 4, 5, 6.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k 3, 4, 5, 6.