Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints (PWCs) – like checking the consistency of a program – are intractable. Many intractable problems in the area of knowledge representation and reasoning have been sho...

We propose an extension of conditional functional dependencies (CFDs), denoted by CFDcs, to express cardinality constraints, domain-specific conventions, and patterns of semantically related constants in a uniform constraint formalism. We show that despite the increased expressive power, the satisfiability and implication problems for CFDcs remain NP-complete and coNP-complete, respectively, th...

The relationship of description logics (DLs) and conceptual modelling has been extensively studied in the literature [5, 4, 1]. One of the advantages of using description logics as modelling languages is that along with their capability of representing knowledge they provide also reasoning services. More precisely, a conceptual model can be represented by a DL ontology (TBox), and standard reas...

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...

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...

A global cardinality constraint (gcc) is speciied in terms of a set of variables X = fx1;:::;xpg which take their values in a subset of V = fv1;:::;vdg. It constrains the number of times each value vi 2 V is assigned to a variable in X to be in an interval li; ui]. A gcc with costs (costgcc) is a generalization of a gcc in which a cost is associated with each value of each variable. Then, each ...

We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to maximize a monotone submodular function while ensuring feasibility. For our results, we assume that we are given an offline algorithm computing an α-approxima...

We study a bin packing problem in which a bin can contain at most k items of total size at most 1, where k ≥ 2 is a given parameter. Items are presented one by one in an online fashion. We analyze the best absolute competitive ratio of the problem and prove tight bounds of 2 for any k ≥ 4. Additionally, we present bounds for relatively small values of k with respect to the asymptotic competitiv...

In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a cnf formula, and we discuss about the relevance of these encodings. We also propose models to facilitate analysis and design of cnf encodings for Boolean constraints.