Covering arrays have been studied for their applications to drug screening and software and hardware testing. In this paper, we model the problem as a constraint program. Our proposed models exploit non-binary (global) constraints, redundant modelling, channelling constraints, and symmetry breaking constraints. Our initial experiments show that with our best integrated model, we are able to eit...

Given a set of polyhedral cones C1, · · · , Ck ⊂ R, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire R or a given linear subspace R. As a consequence, we show that it is coNP-complete to decide if ...

In this paper, a new priority M/M/c queuing hub covering problem is presented, in which products with high priority are selected for service ahead of those with low priority. In addition, a mixed-integer nonlinear mathematical programming model is presented to find a good solution of the given problem. Due to its computational complexity, we propose a multi-objective parallel simulated annealin...

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...

In 1914 Lebesgue defined a ‘universal covering’ to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pál, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen’...