Parallel MUS extraction

Abstract

Parallelization is a natural direction towards the improvements in the scalability of algorithms for the computation of Minimally Unsatisfiable Subformulas (MUSes), and group-MUSes, of CNF formulas. In this paper we propose and analyze a number of approaches to parallel MUS computation. Just as it is the case with the parallel CDCL-based SAT solving, the communication, i.e. the exchange of learned clauses between the solvers running in parallel, emerges as an important component of parallel MUS extraction algorithms. However, in the context of MUS computation the communication might be unsound. We argue that the assumption-based approach to the incremental CDCL-based SAT solving is the key enabling technology for effective sound communication in the context of parallel MUS extraction, and show that fully unrestricted communication is possible in this setting. Furthermore, we propose a number of techniques to improve the quality of communication, as well as the quality of job distribution in the parallel MUS extractor. We evaluate the proposed techniques empirically on industrially-relevant instances of both plain and group MUS problems, and demonstrate significant (up to an order of magnitude) improvements due to the parallelization. © 2013 Springer-Verlag.