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

Kaoru WATANABE; Hiroshi TAMURA; Masakazu SENGOKU

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

Kaoru WATANABE, Hiroshi TAMURA, Masakazu SENGOKU

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.9 pp.1495-1503

Publication Date: 1996/09/25

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Type of Manuscript: PAPER

Category: Graphs and Networks

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Kaoru WATANABE, Hiroshi TAMURA, Masakazu SENGOKU, "The Problem of where to Locate p-Sinks in a Flow Network: Complexity Approach" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 9, pp. 1495-1503, September 1996, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_9_1495/_p

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@ARTICLE{e79-a_9_1495,
author={Kaoru WATANABE, Hiroshi TAMURA, Masakazu SENGOKU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Problem of where to Locate p-Sinks in a Flow Network: Complexity Approach},
year={1996},
volume={E79-A},
number={9},
pages={1495-1503},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - The Problem of where to Locate p-Sinks in a Flow Network: Complexity Approach
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1495
EP - 1503
AU - Kaoru WATANABE
AU - Hiroshi TAMURA
AU - Masakazu SENGOKU
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1996
AB - 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.
ER -