The Problem of where to Locate p-Sinks in a Flow Network: Complexity Approach

Hiroshi TAMURA
Masakazu SENGOKU

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A    No.9    pp.1495-1503
Publication Date: 1996/09/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Graphs and Networks
location problem,  flow network,  NP-complete,  optimization problem,  

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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 show complexity results of the p-collection problem. We prove that the decision problem corresponding to the p-collection problem is strongly NP-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-complete. And we show a polynomial time algorithm for the subproblem of the p-collection problem such that the degree sum of vertices with degree3 in a network, is bound to some constant K0.