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2015•Journal of Applied and Industrial MathematicsRequires access

The maximum flow problem in a network with special conditions of flow distribution

V. A. Skorokhodov, A. S. Chebotareva

Open publisher page 13 citations

Abstract

We consider the problem of finding a maximum flow in networks with strictly and nonstrictly determined flow distribution. We show that, for each condition of flow distribution, a solution to the problem under consideration exists and is unique. Some algorithms for finding a maximum flow are developed for each condition of flow distribution. We find bounds for the maximum flow value in networks with strict flow distribution.

About this research paper

What this paper is about

We consider the problem of finding a maximum flow in networks with strictly and nonstrictly determined flow distribution. We show that, for each condition of flow distribution, a solution to the problem under consideration exists and is unique. Some algorithms for finding a maximum flow are developed for each condition of flow distribution. We find bounds for the maximum flow value in networks with strict flow distribution.

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We consider the problem of finding a maximum flow in networks with strictly and nonstrictly determined flow distribution. We show that, for each condition of flow distribution, a solution to the problem under consideration exists and is unique. Some algorithms for finding a maximum flow are developed for each condition of flow distribution. We find bounds for the maximum flow value in networks with strict flow distribution.

Key concepts: Flow (mathematics), Mathematics, Maximum flow problem, Multi-commodity flow problem, Distribution (mathematics), Flow network, Minimum-cost flow problem, Mathematical optimization

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