Simplifications and speedups of the pseudoflow algorithm
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double-spaced-pseudoflowMar2012.pdf
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575.47 KB
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Adobe PDF
Checksum (MD5)
453460198ceb0df7855477080972e078
Author(s)
Hochbaum, Dorit S.
Orlin, James B.
Date Issued
May 2012
Journal
Networks
Publisher
Wiley Blackwell
Citation
Hochbaum, Dorit S., and James B. Orlin. “Simplifications and Speedups of the Pseudoflow Algorithm.” Networks 61.1 (2013): 40–57.
Version
Author's final manuscript
Abstract
The pseudoflow algorithm for solving the maximum flow and minimum cut problems was devised in Hochbaum (2008). The complexity of the algorithm was shown in (2008) to be O(nm log n). Chandran and Hochbaum, (2009) demonstrated that the pseudoflow algorithm is very efficient in practice, and that the highest label version of the algorithm tends to perform best. Here, we improve the running time of the highest label pseudoflow algorithm to O(n[superscript 3]) using simple data structures and to O(nm log (n[superscript 2]/m)) using the dynamic trees data structure. Both these algorithms use a new form of Depth-First-Search implementation that is likely to be fast in practice as well. In addition, we give a new simpler description of the pseudoflow algorithm by relating it to the simplex algorithm as applied to the maximum preflow problem defined here. The interpretation of the generic pseudoflow algorithm as a simplex-like algorithm for the maximum preflow problem motivates the pseudoflow algorithm and highlights differences between the pseudoflow algorithm and the preflow-push algorithm of Goldberg and Tarjan.
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1002/net.21467
