Diversification and Intensification in Parallel SAT Solving

Abstract

Abstract. In 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 tradeoff, 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.

A Hybrid Paradigm for Adaptive Parallel Search

“…distribute(i) 30: Send signal -1 to all processors A portfolio-based method that shares information must address the trade-off between diversification and intensification [19]. Diversification uses dramatically different search strategies, and expects its searchers to proceed independently.…”

“…In contrast, intensification explores with relatively small variations around a single strategy, and expects to share the information it gathers among all its searchers. Because Spread is intended to solve difficult CSPs, it does intensification in its portfolio phase, as recommended in [19]. Indeed, the primary purpose of Spread's portfolio phase is to glean information to support search space splitting, not to solve P .…”

“…Otherwise, the worker has exhausted its resources r and returns its subproblem to the manager with message 1 (Algorithm 2, line 16). If the subproblem queue has fewer than threshold subproblems, the manager recursively partitions the returned subproblem on new splitting variables, and enqueues the resultant subproblems with their resource limits (Algorithm 3, lines [18][19][20][21][22]. If there is insufficient space on the queue to repartition the subproblem, the manager re-enqueues it as it was, but with a larger resource limit (Algorithm 3, lines 24-26).…”

Modern Cooperative Parallel SAT Solving

“…Furthermore, not only the size of the clause, but also its LBD has been taken into account for sharing clauses [32]. Finally, not only learned clauses, but also active variables and other information has been shared [6,8]. A discussion about the soundness of clause sharing is presented in [34].…”

“…These incarnations of the solving engine all solve the same input instance, and additionally share clauses, that have been learned during their search process. Much research has been done on this type of solvers, for example investigating the properties of clause sharing [6,7], or whether additional information sharing could improve the performance of the parallel SAT solver [6,8]. However, there also exist parallel portfolio solvers that simply combine many solvers with the aim to have a specialized solver for each category of instances, such that the overall portfolio provides a good performance [9].…”