# The discrete optimization problems with interval objective function on graphs and hypergraphs and the interval greedy algorithm

We consider the discrete optimization problems with interval objective function on graphs and hypergraphs. For the problems, we need to find either a strong optimal solution or a set of all possible weak solutions. A strong solution of the problem is a solution that is optimal for all possible values of the objective function's coefficients that belong to predefined intervals. A weak solution is a solution that is optimal for some of the possible values of the coefficients. We characterize the strong solutions for considered problems. We give a generalization of the greedy algorithm for the case of interval objective function. For the discrete optimization problems we consider, the algorithm gives a set of all possible greedy solutions and the set of all possible values of the objective function for the solutions. For a given probability distribution that is defined on coefficients' intervals, we compute probabilities of the weak solutions, expected values of the objective function for them, etc.