Construction of an ROBDD for a PB-Constraint in Band Form and Related Techniques for PB-Solvers

Abstract

SUMMARYPseudo-Boolean (PB) problems are Integer Linear Problem restricted to 0-1 variables. This paper discusses on acceleration techniques of PB-solvers that employ SAT-solving of combined CNFs each of which is produced from each PB-constraint via a binary decision diagram (BDD). Specifically, we show (i) an efficient construction of a reduced ordered BDD (ROBDD) from a constraint in band form l ≤ Linear term ≤ h, (ii) a CNF coding that produces two clauses for some nodes in an ROBDD obtained by (i), and (iii) an incremental SAT-solving of the binary/alternative search for minimizing values of a given goal function. We implemented the proposed constructions and report on experimental results.

Competitive Sorter-based Encoding of PB-Constraints into SAT

“…Abío et al [2] show a construction of Reduced Ordered BDDs (ROBDDs), which produce arc-consistent, efficient encoding for PB-constraints. Sakai and Nabeshima [21] extend the ROBDD construction to support constraints in band form: l ≤ Linear term ≤ h. They also propose an incremental SAT-solving strategy of binary/alternative search for minimizing values of a given goal function and their experiments show significant speed-up in SAT-solver runtime.…”

“…In particular, we use optimal base searching algorithm based on the work of Codish et al [8] and ROBDD structure [2] instead of BDDs for one of the encodings in MiniSat+. We also substitute sequential search of minimal value of the goal function in optimization problems with binary search similarly to Sakai and Nabeshima [21]. We use COMiniSatPS [19] by Chanseok Oh as the underlying SAT-solver, as it has been observed to perform better than the original MiniSat [10] for many instances.…”

“…We experimentally compare our solver with other state-of-the-art general constraints solvers like PBLib [20] and NaPS [21] to prove that our techniques are good in practice. Since more then a decade there have been organized a series of Pseudo-Boolean Evaluations [18] which aim to assess the state-of-the-art in the field of PB-solvers.…”

“…We use the following optimization found in NaPS [21] for simplifying inequality assertions in a constraint. We introduce this concept with an example.…”

“…Sakai and Nabeshima [21] propose the binary strategy for the choice of new k . Let k be the best known goal value and l be the greatest known lower bound, which is initially the sum of negative coefficients of f .…”