In this article, we consider the set covering problem with conflict constraints, i.e., from each conflicting pair of columns at most one column can appear in feasible solution. For problem, propose appropriate pre-processing techniques and several families Valid Inequalities (VIs) for corresponding integer programming model that result simultaneous presence constraints stable (conflict) constra...

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’...

K e y w o r d s S e t c o v e r i n g problems, Fuzzy sets, Fuzzy set-covering problem, Algebraic sum operator. 1. I N T R O D U C T I O N A classical set-covering problem considers the subsets I = {1, 2 , . . . , m} and J = {1, 2 , . . . , n} of integers. A collection p of subset Pj of I is a cover of I, if the union of the members of go is I, i.e., let Pj C I, go = {Pj : j C J0}, J0 C J, go i...