Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...

In this paper, we develop a uniied approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings deened in Marshall and Olkin, by deening a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing determin...

The most popular approach to decision-making in the setting of fuzzy sets is the maximin ranking of solutions. This method is natural when interpreting the fuzzy sets as flexible constraints that cannot compensate with one another. However the obtained ranking of solutions is very coarse. Two kinds of refinements to this ordering are introduced: a partial ordering according to the least satisfi...

Multiobjective optimization problems with a variable ordering structure instead of a partial ordering have recently gained interest due to several applications. In the last years a basic theory has been developed for such problems. The difficulty in their study arises from the fact that the binary relations of the variable ordering structure, which are defined by a cone-valued map which associa...

Graph-based learning methods explicitly consider the relations between two entities (i.e., vertices) for learning the prediction function. They have been widely used in semi-supervised learning, manifold ranking, and clustering, among other tasks. Enhancing the expressiveness of simple graphs, hypergraphs formulate an edge as a link to multiple vertices, so as to model the higher-order relation...

We introduce an optimality theory for finite impulse response (FIR) filterbanks using a general algebraic point of view. We consider an admissible set of FIR filterbanks and use scalability as the main notion based on which performance of the elements in are compared. We show that quantification of scalability leads naturally to a partial ordering on the set . An optimal solution is, therefore,...