THE PROBLEM OF WHERE TO LOCATE P-SINKS IN A FLOW NETWORK - COMPLEXITYAPPROACH

The p-collection problem is where to locate p sinks in a flow network such that the value of a maximum flow is maximum. In this paper we sho w complexity results of the p-collection problem. We prove that the de cision problem corresponding to the p-collection problem is strongly N P-complete. Although location problems (the p-center problem and the p -median problem) in networks and flow networks with tree structure is solvable in polynomial time, we prove that the decision problem of the p-collection problem in networks with tree structure, is weakly NP-co mplete. And we show a polynomial lime algorithm for the subproblem of the p-collection problem such that the degree sum of vertices with deg ree greater than or equal to 3 in a network, is bound to some constant K greater than or equal to 0.