Optimum flows in general communication networks

Onaga, Kenji

doi:10.1016/0016-0032(67)90046-4

Cited by 48 publications

(20 citation statements)

References 2 publications

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“…Generalized circulation problem has been studied extensively in the 60's and early 70`s 5,9,22,25,26,33]. This problem can be used to model many situations which are impossible to express using standard network ows (see e.g., 8,22]).…”

Section: Introductionmentioning

confidence: 99%

Combinatorial Algorithms for the Generalized Circulation Problem

1991

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We consider a generalization of the maximum ow problem in which the amounts of ow entering and leaving an arc are linearly related. More precisely, if x(e) units of ow enter an arc e, x(e) (e) units arrive at the other end. For instance, nodes of the graph can correspond to di erent currencies, with the multipliers being the exchange rates. We require conservation of ow at every node except a given source node. The goal is to maximize the amount of ow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. In this paper we present the rst polynomial time combinatorial algorithms for this problem. The algorithms are simple and intuitive.

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Section: Introductionmentioning

confidence: 99%

Combinatorial Algorithms for the Generalized Circulation Problem

1991

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“…Since the path → → → is the minimum loss path and path → → → is the highest loss path according to the SSPA presented by Onaga [13,14]. Now the Fig.…”

Section: Generalized Dynamic Flow On Lossy Networkmentioning

confidence: 95%

Generalized Dynamic Flow on Lossy Network

Gautam

Pyakurel

Dhamala

2019

J. Inst. Engineering

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Despite of implicit flow conservation on every arc of traditional network flow model, the generalized network flow model assumes the proportional and symmetric loss factor on each arc. This paper considers two terminal lossy networks specifying the portion of flow entering an arc at its tail node that reaches to its head node. We studied the generalized maximum continuous dynamic contraflow (GMCDCF) and generalized continuous earliest arrival contraflow (GCEACF) problems. The problems are efficiently solved with pseudo-polynomial time algorithms. Moreover, a fully polynomial time approximation scheme (FPTAS) is proposed in polynomial time.

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“…For alternative formulations of the generalized circulation problem, see e.g., [7,17]. The generalized circulation problem is closely related to the minimum-cost circulation problem [20,28]. When discussing the minimum-cost circulation problem, we follow the notation of [SI.…”

Section: Definitions and Backgroundmentioning

confidence: 99%

“…Theorem 2.1 [20] A generalized circulation is optimal if and only if its residual graph contains no GAPS.…”

Section: (5)mentioning

confidence: 99%

Combinatorial algorithms for the generalized circulation problem

Goldberg

Plotkin²,

Tardos

1988

[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science

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We consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if z(e) units of flow enter an arc e, z(e)r(e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. We require conservation of flow at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. In this paper we present the first polynomial time combinatorial algorithms for this problem. The algorithms are simple and intuitive.

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Optimum flows in general communication networks

Cited by 48 publications

References 2 publications

Combinatorial Algorithms for the Generalized Circulation Problem

Combinatorial Algorithms for the Generalized Circulation Problem

Generalized Dynamic Flow on Lossy Network

Combinatorial algorithms for the generalized circulation problem

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