Abstract
AbstractAs location problems in flow networks, there are p‐center and p‐median problems; and they are known to be solvable in polynomial time. In this paper, we propose a new location problem. It is the problem of locating p‐sinks so that the maximum flow is maximized given a flow network N with a source (this problem is called a p‐collection problem). First, a linear time algorithm to solve the 1‐collection problem for trees is given. Then a pseudo‐polynomial time algorithm to solve the p‐collection problem for trees based on dynamic programming is presented. Since the decision problem corresponding to the p‐collection problem for trees is known to be NP‐complete, its decision problem turns out to be strongly NP‐complete.
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