A computational study of the capacity scaling algorithm for the maximum flow problem

Authors:
Cenk Çalışkan
Affiliations:
Department of Finance and Economics, Woodbury School of Business, Utah Valley University, Orem, UT 84058, United States
Venue:
Computers and Operations Research
Year:
2012

Citing 6
Cited 0

A new approach to the maximum flow problem

STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A new approach to the maximum-flow problem

Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications

Network flows: theory, algorithms, and applications
Beyond the flow decomposition barrier

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Network Flows and Matching: First DIMACS Implementation Challenge
A generalization of the scaling max-flow algorithm

Computers and Operations Research

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Abstract

The capacity scaling algorithm for the maximum flow problem runs in O(nmlogU) time where n is the number of nodes, m is the number of arcs, and U is the largest arc capacity in the network. The two-phase capacity scaling algorithm reduces this bound to O(nmlog(U/n)). This running time is achieved with the restriction that flows are pushed on individual arcs while paths are being identified, but this causes slower empirical run times compared to the single-phase capacity scaling algorithm. In this research, we prove that the two-phase algorithm runs in the same theoretical time without the mentioned restriction. We also show that in practice, it runs significantly faster than the single-phase capacity scaling algorithm.