On a generalization of a covering problem on undirected flow networks

Location theory on networks is concerned with the problem of selecting the best location in a specified network for facilities. Many studies for the theory have been done. We have studied location theory from the standpoint of measuring the closeness between two vertices by the capacity (maximum flow value) between two vertices. In the previous paper, we have considered location problems, called covering problems and proposed polynomial time algorithms for these problems. These problems are applicable to assigning files to some computers in a computer network. This paper concerns a problem called plural cover problem. We define a generalized plural cover problem and we propose an efficient algorithm for the generalized plural cover problem.