In the entity-relationship approach to database design, integrity constraints are used to express database semantics. Cardinality constraints are a frequently used way of imposing restrictions to the structure of the databases. In this paper, we consider additive cardinality constraints which specify lower and upper bounds on the total number of relationships an entity of a xed type may be invo...

ISA and cardinality constraints are among the most interesting types of constraints in data models. ISA constraints are used to establish several forms of containment among classes, and are receiving great attention in moving to object-oriented data models, where classes are organized in hierarchies based on a generalization/specialization principle. Cardinality constraints impose restrictions ...

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in general when there exist multiple overlapped cardiaiality constraints. In this ...

Tracking a financial index boils down to replicating its trajectory of returns for well-defined time span by investing in weighted subset the securities included benchmark. Picking optimal combination assets becomes challenging NP-hard problem even moderately large indices consisting dozens or hundreds assets, thereby requiring heuristic methods find approximate solutions. Hybrid quantum-classi...

In this paper, we address the encoding into CNF clauses of Boolean cardinality constraints that arise in many practical applications. The proposed encoding is efficient with respect to unit propagation, which is implemented in almost all complete CNF satisfiability solvers. We prove the practical efficiency of this encoding on some problems arising in discrete tomography that involve many cardi...

Traditional SAT-based MaxSAT solvers encode cardinality constraints directly as part of the CNF and solve the entire optimization problem by a sequence of iterative calls of the underlying SAT solver. The main drawback of such approaches is their dependence on the number of soft clauses: The more soft clauses the MaxSAT instance contains, the larger is the CNF part encoding the cardinality cons...

Selection comparator networks have been studied for many years. Recently, they have been successfully applied to encode cardinality constraints for SAT-solvers. To decrease the size of generated formula there is a need for constructions of selection networks that can be efficiently generated and produce networks of small sizes for the practical range of their two parameters: n – the number of i...

We present a partial Max-SAT solver QMaxSAT which uses CNF encoding of Boolean cardinality constraints. The old version 0.1 was obtained by adapting a CDCL based SAT solver MiniSat to manage cardinality constraints. It was placed first in the industrial subcategory and second in the crafted subcategory of partial Max-SAT category of the 2010 Max-SAT Evaluation. The new version 0.2 is obtained b...

Although a large number of queries used in applications ranging from web search to business intelligence have associated cardinality constraints, current database engines have minimal support for ensuring query cardinality. This leads to two main types of problems: the empty result-set problems and the too few/too many problems. Inability to meet query cardinality constraints requires the user ...