The problem of maximum flow with minimum attainable cost in a network

Ahmed, Nazimuddin; Das, S.; Purusotham, S.

doi:10.1007/s12597-012-0106-1

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…e time-varying wastage maximum flow problem is the maximum flow problem with time-varying arc capacities and additive flow losses on the arcs, which can be applied to intelligent transportation [12,13], communication network [14], financial analysis [15,16], and other fields. In financial networks, Eboli [17] has described the balance-sheet as a loss flow on the arc.…”

Section: Introductionmentioning

confidence: 99%

A Novel Maximum Flow Algorithm with Neural Network for Time-Varying Wastage Networks

Zhang

Jiang

Huang

2022

Security and Communication Networks

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This paper introduces a time-varying wastage maximum flow problem (TWMFP) and proposes a time-flow neural network (TFNN) for solving the TWMFPs. The time-varying wastage maximum flow problem is concerned with finding the maximum flow in a network with time-varying arc capacities and additive flow losses on the arcs. This problem has multiple applications in transportation, communication, and financial network. For example, solving the maximum traffic flow of the transportation network and the maximum profit of the financial network. Unlike traditional neural network algorithms, the proposed TFNN does not require any training by means of its time-flow mechanism. The time-flow mechanism is realized by each active neuron sending pulses to its successor neurons. In order to maximize the network flow, the proposed TFNN can be divided into two parts: path-pulse neural networks (PPNNs) and subnet-flow neural networks (SFNN). PPNN is to generate two subnet sets (viz. with wastage arcs and without), and SFNN is to find the maximum flow value of each subnet. The subnet computing strategy of the proposed algorithm greatly improves the solution accuracy of TWMFPs. Theoretical analysis and experiments have proved the effectiveness of TFNN. The experiment results of the transportation network (viz. New York Road) show that the proposed TFNN has better performance (viz. error rate and computational time) compared to classical algorithms.

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Section: Introductionmentioning

confidence: 99%

A Novel Maximum Flow Algorithm with Neural Network for Time-Varying Wastage Networks

Zhang

Jiang

Huang

2022

Security and Communication Networks

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“…Rajalakshmi and Vaidyanathan (2019) applied Edmonds-Karp maximum flow algorithm to traffic management system, so as to minimize congestion by finding alternative routes and traffic flow regulating. Ahmed et al (2013) introduced lexicographic search technique to obtain exact solutions to the problem of maximum flow with minimum attainable cost in a flow network. Their computational experiments revealed that the proposed algorithm computes the maximum flow value in any given network in the least time.…”

Section: Motivationmentioning

confidence: 99%

Extreme Min – Cut Max – Flow Algorithm

Tawanda

Nyamugure

Munapo

et al. 2023

International Journal of Applied Metaheuristic Computing

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In this article, the authors propose a maximum flow algorithm based on flow matrix. The algorithm only requires the effort to reduce the capacity of the underutilized arcs to that of the respective flow. The optimality of the algorithm is proved by the max-flow min-cut theorem. The algorithm is table-based, thus avoiding augmenting path and residual network concepts. The authors used numerical examples and computational comparisons to demonstrate the efficiency of the algorithm. These examples and comparisons revealed that the proposed algorithm is capable of computing exact solutions while using few iterations as compared to some existing algorithms.

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“…[12] [13] studied the optimization problem of oil distribution based on the minimum cost flow theory. [14] obtained an optimal route of a more realistic situation as to scheduling maximum flows at a minimum cost from a source to a destination. Several special cases of the problem were intensively studied in the literature and were solved by the proposed various techniques.…”

Section: Introductionmentioning

confidence: 99%

Application of Graph Theory in Grain and Oil Deployment

Xu¹,

Song²

2015

JSSM

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The deployment of grain and oil is related to the daily needs of people and the stability of society. In this paper, we take the shortest path problem and the minimum cost maximum flow problem in graph theory as the theoretical basis. Through the establishment of distance matrix between the reserves station and the deployment warehouse or between reserve station and reserve station, we use the Floyd algorithm to calculate the shortest path between any two points in the matrix to determine the optimal deployment of the emergency plan. Through the establishment of mathematical model of the reserve station and deployment warehouse, we use the minimum cost maximum flow theory to solve the model and to obtain the deployment programs of grain and oil under normal circumstances. Through the combination of shortest path and minimum cost and maximum flow, we give the deployment plan under the general emergency situation and provide a new way for the deployment of the supply of grain and oil in each case.

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The problem of maximum flow with minimum attainable cost in a network

Cited by 4 publications

References 12 publications

A Novel Maximum Flow Algorithm with Neural Network for Time-Varying Wastage Networks

A Novel Maximum Flow Algorithm with Neural Network for Time-Varying Wastage Networks

Extreme Min – Cut Max – Flow Algorithm

Application of Graph Theory in Grain and Oil Deployment

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