Diversification and Intensification in Parallel {SAT} Solving

International audienceIn this paper, we explore the two well-known principles of diversification and intensification in portfolio-based parallel SAT solving. These dual concepts play an important role in several search algorithms including local search, and appear to be a key point in modern parallel SAT solvers. To study their trade-off, we define two roles for the computational units. Some of them classified as Masters perform an original search strategy, ensuring diversification. The remaining units, classified as Slaves are there to intensify their master's strategy. Several important questions have to be answered. The first one is what information should be given to a slave in order to intensify a given search effort? The second one is, how often, a subordinated unit has to receive such information? Finally, the question of finding the number of subordinated units along their connections with the search efforts has to be answered. Our results lead to an original intensification strategy which outperforms the best parallel SAT solver, and solves some open SAT instances

PARTITIONING SEARCH SPACES OF A RANDOMIZED SEARCH

This work studies the following question: given an instance of the propositional satisfiability problem, a randomized satisfiability solver, and a cluster of n computers, what is the best way to use the computers to solve the instance? Two approaches, simple distribution and search space partitioning as well as their combinations are investigated both analytically and empirically. It is shown that the results depend heavily on the type of the problem (unsatisfiable, satisfiable with few solutions, and satisfiable with many solutions) as well as on how good the search space partitioning function is. In addition, the behavior of a real search space partitioning function is evaluated in the same framework. The results suggest that in practice one should combine the simple distribution and search space partitioning approaches

A distribution method for solving SAT in grids

Abstract. The emerging large-scale computational grid infrastructure is providing an interesting platform for massive distributed computations. In this paper the problem of exploiting such computational grids for solving challenging propositional satisfiability problem (SAT) instances is studied. When designing a distributed algorithm for a large loosely coupled computational grid, a number of grid specific problems need to be tackled including the heterogeneity of the resources, inherent communication delays, and high failure probabilities of grid jobs. In this work a novel distribution method for solving SAT problem instances, called scattering, is introduced. The key advantages of scattering are that it can be used in conjunction with any sequential SAT solver (including industrial black box solvers), the distribution heuristic is strictly separated from the heuristic used in sequential solving, and it requires no communication between processes solving subproblems but still allows coordination of such processes. An implementation of the method has been developed for NorduGrid, a large widely distributed production-level grid running in Scandinavia. The implementation has been benchmarked with test cases including random 3SAT and challenging industrial benchmarks used in previous SAT competitions.

Modular and Efficient Divide-and-Conquer SAT Solver on Top of the Painless Framework

International audienceOver the last decade, parallel SATisfiability solving has been widely studied from both theoretical and practical aspects. There are two main approaches. First, divide-and-conquer (D&C) splits the search space, each solver being in charge of a particular subspace. The second one, portfolio launches multiple solvers in parallel, and the first to find a solution ends the computation. However although D&C based approaches seem to be the natural way to work in parallel, portfolio ones experimentally provide better performances. An explanation resides on the difficulties to use the native formulation of the SAT problem (i.e., the CNF form) to compute an apriori good search space partitioning (i.e.,all parallel solvers process their sub-spaces in comparable computational time). To avoid this, dynamic load balancing of the search subspaces is implemented. Unfortunately, this isdifficult to compare load balancing strategies since state-of-the-art SAT solvers appropriately dealing with these aspects are hardly adaptable tovarious strategies than the ones they have been designed for. This paper aims at providing a way to overcome this problem by proposing an implementation and evaluation of different types of divide-and-conquer inspired from the literature. These are relying on thePainless framework, which provides concurrent facilities to elaborate such parallel SAT solvers. Comparison of the various strategies are thendiscussed

Partitioning SAT Instances for Distributed Solving

Abstract. In this paper we study the problem of solving hard propositional satisfiability problem (SAT) instances in a computing grid or cloud, where run times and communication between parallel running computations are limited. We study analytically an approach where the instance is partitioned iteratively into a tree of subproblems and each node in the tree is solved in parallel. We present new methods which combine clause learning and look-ahead to construct partitions, evaluate their efficiency experimentally, and finally demonstrate the power of the approach in a real grid environment by solving several instances that were not solved in a SAT solver competition.