We study a generalized distributionally robust chance-constrained set covering problem (DRC) with Wasserstein ambiguity set, where both decisions and uncertainty are binary-valued. establish the NP-hardness of DRC recast it as two-stage stochastic program, which facilitates decomposition algorithms. Furthermore, we derive two families valid inequalities. The first family targets hypograph “shif...

We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm is based on a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set, the minimal upward covering set and the minimal down...

We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has focused on the special case in which uncertainties are independent. In this paper, we formulate c...

We propose a new branch-and-bound algorithm to solve hard instances of set covering problems arising from Steiner triple systems.

Flying Elephants (FE) is a generalization and a new interpretation of the Hyperbolic Smoothing approach. The article introduces the fundamental smoothing procedures. It presents a general overview of successful applications of the approach for solving a select set of five important problems, namely: distance geometry, covering, clustering, Fermat-Weber and hub location. For each problem it is p...