2 research outputs found
Encoding Cardinality Constraints using Generalized Selection Networks
Boolean cardinality constraints state that at most (at least, or exactly)
out of propositional literals can be true. We propose a new class of
selection networks that can be used for an efficient encoding of them. Several
comparator networks have been proposed recently for encoding cardinality
constraints and experiments have proved their efficiency. Those were based
mainly on the odd-even or pairwise comparator networks. We use similar ideas,
but we extend the model of comparator networks so that the basic components are
not only comparators (2-sorters) but more general -sorters, for .
The inputs are organized into columns, in which elements are recursively
selected and, after that, columns are merged using an idea of multi-way
merging. We present two algorithms parametrized by . We call those
networks -Wise Selection Network and -Odd-Even Selection Network. We give
detailed construction of the mergers when . The construction can be
directly applied to any values of and . The proposed encoding of sorters
is standard, therefore the arc-consistency is preserved. We prove correctness
of the constructions and present the theoretical and experimental evaluation,
which show that the new encodings are competitive to the other state-of-art
encodings
Solving MaxSAT by Successive Calls to a SAT Solver
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth
assignment that maximizes the number of satisfied clauses of a given Boolean
formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have
been developed during recent years, and many of them were presented in the
well-known SAT conference. Algorithms for MaxSAT generally fall into two
categories: (1) branch and bound algorithms and (2) algorithms that use
successive calls to a SAT solver (SAT- based), which this paper in on. In
practical problems, SAT-based algorithms have been shown to be more efficient.
This paper provides an experimental investigation to compare the performance of
recent SAT-based and branch and bound algorithms on the benchmarks of the
MaxSAT Evaluations.Comment: Survey, 46 page