As location problems in flow networks, there are p-center and p-median problems;and they are known to be solvable in polynomialtime. In this paper, we propose a new location problem. It is the problem of locating p-s...
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As location problems in flow networks, there are p-center and p-median problems;and they are known to be solvable in polynomialtime. 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 timealgorithm 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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