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Simplifications and speedups of the pseudoflow algorithm
Author(s) -
Hochbaum Dorit S.,
Orlin James B.
Publication year - 2013
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21467
Subject(s) - algorithm , simplex algorithm , maximum flow problem , computer science , dinic's algorithm , simple (philosophy) , simple algorithm , out of kilter algorithm , time complexity , mathematics , mathematical optimization , linear programming , theoretical computer science , dijkstra's algorithm , graph , philosophy , physics , epistemology , shortest path problem , thermodynamics
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 3 ) using simple data structures and to O ( nm log ( n 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. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013