Weakening Cardinality Constraints Creates Harder Satisfiability Benchmarks

Sets with Cardinality Constraints in Satisfiability Modulo Theories

Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier-free BAPA (QFBAPA). In contrast to many other NP-complete problems (such as quantifier-free first-order logic or linear arithmetic), the appl...

On Sets with Cardinality Constraints in Satisfiability Modulo Theories

Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier-free BAPA (QFBAPA). Deciding the satisfiability of QFBAPA formulas has been shown to be NP-complete using an eager reduction to quantifier-fr...

Adding cardinality constraints to integer programs with applications to maximum satisfiability

Max-SAT-CC is the following optimization problem: Given a formula in CNF and a bound k, find an assignment with at most k variables being set to true that maximizes the number of satisfied clauses among all such assignments. If each clause is restricted to have at most ` literals, we obtain the problem Max-`SAT-CC. Sviridenko (Algorithmica, 30(3):398–405, 2001) designed a (1− e−1)-approximation...

Cardinality Constraints in

Submodular Maximization with Cardinality Constraints

We consider the problem of maximizing a (non-monotone) submodular function subject to a cardinality constraint. In addition to capturing well-known combinatorial optimization problems, e.g., Maxk-Coverage and Max-Bisection, this problem has applications in other more practical settings such as natural language processing, information retrieval, and machine learning. In this work we present impr...