In this paper, the authors consider the network version of the m-median problem with mutual communication (MMMC). They reformulate this problem as a graph theoretic node selection problem defined on a special graph. The authors give a polynomial time algorithm to solve the node selection problem when the flow graph (graph that denotes the interaction between pairs of new facilities in MMMC) has a special structure. They also show that with some modification in the algorithm for MMC, the m-center problem with mutual communication can also be solved when the flow graph has a special structure.
