A satissability problem can be regarded as a nondisjoint union of set covering problems. We show that if the resolution method of theorem proving is applied to the satissability problem, its constraint set deenes an integral polytope if and only if the constraint sets of the set covering problems do. In this sense, resolution reduces the integrality question for the satissability problem to tha...

We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields such as (i) G is definably an almost direct product of a semisimple group and a commutative group, (ii) (G, ·) is elementarily equivalent to (G/G, ·). We also prove results on the internality of finite covers of G in an o-minimal environment, as well as deducing the full compact domin...

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’...

The set covering problem is a formal model for many practical optimization problems. In the set covering problem the goal is to choose a subset of the columns of minimal cost that covers every row. Here, we present a novel application of the artificial bee colony algorithm to solve the non-unicost set covering problem. The artificial bee colony algorithm is a recent swarm metaheuristic techniqu...

in this paper, a robust model presented is developed for hub covering flow problem in which hubs have capacity. this problem has two objective functions converting to a single-objective problem by using weighting method. firstly, the problem will be formulated in a certain case. then, by considering the demand as a non-random variable, it will be modeled by robust optimization. finally, by usin...

The problem of covering edges and vertices in a graph (or in a hypergraph) was motivated by a problem arising in the context of the component assembly problem. The problem is as follows: given a graph and a clique size k, find the minimum number of k-cliques such that all edges and vertices of the graph are covered by (included in) the cliques. This paper provides a collection of approximation ...