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.

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper investigates development of a local branching approach for the SCP. This solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. The algorithm parameters are tuned by design of experiments approach. The proposed method is te...