An entity relationship diagram (ERD) shows the cardinality of each entity in a relationship. In an ERD, minimum cardinalities can be either 0 or 1, and maximum cardinalities can be 1 or infinity. Bounded cardinality occurs when a relationship between entities has cardinality within a specified range. Problems displaying bounded cardinality might include team rosters that must have exactly 5, 9,...

Many portfolio optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio optimization. In addition, one of the main concerns with most portfolio optimization is associated with the type of constraints considered in different models. In many cases, the resulted p...

In this work, we study constrained clustering, where some constraints are utilized to guide the clustering process. In existing work on this topic, two main categories of constraints have been explored, namely pairwise and cardinality constraints. Pairwise constraints enforce that the cluster labels of two instances be the same (must-link constraints) or different (cannot-link constraints). Car...

Optimality Theory assumes the candidate set generated for any given input is of infinite cardinality. If all of the candidates in the candidate set were potential winners (optimal candidates under some ranking), then OT would have predicted an infinite typology— there would be infinitely many possible languages. However, Samek-Lodovici and Prince (1999) have shown that in standard OT (with only...

Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variablesM, with the same constraint defined by a finitestate automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The fi...

This report bases itself on the idea of using concrete examples to verify conceptual schemas, and in particular cardinality constraints. When novice ORM modellers model domains, the selection of proper cardinality constraints for relationship types is quite often prone to errors. In this report we propose a mechanism for the generation of significant examples for selected subschemas. The genera...

Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate properties: relationships between the typestates of objects can be expressed as subset and disjointness relations on sets, and elements of sets can be represe...