Boolean cardinality constraints are commonly translated (encoded) into Boolean CNF, a standard form for Boolean satisfiability problems, which can be solved using a standard SAT solving program. However, cardinality constraints are a simple generalization of clauses, and the complexity entailed by encoding them into CNF can be avoided by reasoning about cardinality constraints natively within a...

investment plays a vital role on economic growth. one of the main objectives of all countries is to achieve sustainable economic growth and development. nowadays, a considerable amount of activities performed by the managers and investors in general is to make a portfolio of assets effectively meeting demand goals. in this study, mean-variance markowitz model by cardinality constraints and also...

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...

We present novel approaches to detect cardinality constraints expressed in CNF. The first approach is based on a syntactic analysis of specific data structures used in SAT solvers to represent binary and ternary clauses, whereas the second approach is based on a semantic analysis by unit propagation. The syntactic approach computes an approximation of the cardinality constraints AtMost-1 and At...