A bit-arc capacity scaling algorithm for the maximum flow problem subjected to box constraints on the flow vector in digraph

A bit-arc capacity scaling algorithm to solve the maximal flow problem subjected to box constraints on the flow vector in directed network has been presented. The algorithm is mainly based on successive divisions of capacities by multiples of two. It solves the maximal flow problem as a sequence of...

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Bibliographic Details
Published in:Network biology Vol. 15; no. 2; pp. 48 - 66
Main Author: Tlas, Muhammad
Format: Journal Article
Language:English
Published: Hong Kong International Academy of Ecology and Environmental Sciences (IAEES) 01.06.2025
International Academy of Ecology and Environmental Sciences
Subjects:
Algorithms
augmenting path method
Biology
Constraints
digraph
Graph theory
Labeling
Maximum flow
maximum flow problem
network flow
Nodes
polynomial time algorithm
scaling algorithm
Shortest-path problems
ISSN:2220-8879
Online Access:Get full text
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Summary:A bit-arc capacity scaling algorithm to solve the maximal flow problem subjected to box constraints on the flow vector in directed network has been presented. The algorithm is mainly based on successive divisions of capacities by multiples of two. It solves the maximal flow problem as a sequence of O(n2) Dijkstra's shortest path between two nodes in the defined residual network with n nodes and m arcs. It is proven that, the algorithm's complexity was estimated to be no more than O(n2mr) arithmetic operations in the worst case to reach the maximum vector flow through the directed network. Where r denotes to the smallest integer greater than or equal to log B, and B denotes to the largest arc capacity of the network. A numerical example has been illustrated using the proposed algorithm.
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ISSN:2220-8879