We consider a one dimensional storage system where each container can store a bounded amount of capacity as well as a bounded number of items k ≥ 2. This defines the (standard) bin packing problem with cardinality constraints which is an important version of bin packing, introduced by Krause, Shen and Schwetman already in 1975. Following previous work on the unbounded space online problem, we e...

Cardinality constrained bin packing or bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k ≥ 2, items having sizes in (0, 1] associated with them are presented one by one to be packed into unit capacity bins, such that the capacities of bins are not exceeded, and no bin receives more than k items. We resolve the online problem in t...

Probabilistic cardinality constraints stipulate lower bounds on the marginal probability of cardinality constraints in probabilistic databases. The demo shows how the computation of Armstrong PCsketches helps design teams identify lower bounds that separate meaningful from meaningless probabilistic databases in an application domain.

Applications in software verification and interactive theorem proving often involve reasoning about sets of objects. Cardinality constraints on such collections also arise in these scenarios. Multisets arise for analogous reasons as sets: abstracting the content of linked data structure with duplicate elements leads to multisets. Interactive theorem provers such as Isabelle specify theories of ...

We present for the first-order theory of atomic Boolean algebras of sets with linear cardinality constraints a quantifier elimination algorithm. In the case of atomic Boolean algebras of sets, this is a new generalization of Boole’s well-known variable elimination method for conjunctions of Boolean equality constraints. We also explain the connection of this new logical result with the evaluati...

Generalized itemset mining is an established data mining technique that focuses on discovering high-level correlations among large databases. By exploiting a taxonomy built over the data items, items are aggregated into higher level concepts and, thus, data correlations at different abstraction levels can be discovered. However, since a large number of patterns can be extracted, the result of t...

XML has gained widespread acceptance as a premier format for publishing,sharing and manipulating data through the web. While the semi-structured na-ture of XML provides a high degree of syntactic flexibility there are significantshortcomings when it comes to specifying the semantics of XML data. For theadvancement of XML applications it is therefore a major challenge to disc...

Numerical dependencies (NDs) are a type of database constraints in which one limits the number of distinct Y -values that can appear together with any X-value, where both X and Y are sets of attributes. The seminal work by Grant and Minker has shown that NDs are not finitely axiomatizable, which has cut further investigation on this kind of constraints. In this paper we show that, given a set o...

This paper continues the study of the the allocation of memory to processors in a pipeline problem. This problem can be modeled as a variation of bin packing where each item corresponds to a different type and the normalized weight of each item can be greater than 1, which is the size of a bin. Furthermore, in this problem, items may be split arbitrarily, but each bin may contain at most k type...

A cardinality constraint imposes that each value of a set V must be taken a certain number of times by a set of variables X, whereas an among constraint imposes that a certain number of variables of a set X must take a value in the set V. This paper studies several combinations of among constraints and several conjunctions of among constraints and cardinality constraints. Some filtering algorit...