Abstract
We study the maximum-flow algorithm of Goldberg and Tarjan and show that the largest-label implementation runs inO(n 2 √m) time. We give a new proof of this fact. We compare our proof with the earlier work by Cheriyan and Maheswari who showed that the largest-label implementation of the preflow-push algorithm of Goldberg and Tarjan runs inO(n 2 √m) time when implemented with current edges. Our proof that the number of nonsaturating pushes isO(n 2 √m), does not rely on implementing pushes with current edges, therefore it is true for a much larger family of largest-label implementation of the preflow-push algorithms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Cheriyan, T. Hagerup, and K. Mehlhorn, Can a Maximum Flow be Computed ino(nm) Time?,Proceedings of the 17th International Colloquium on Automata, Languages, and Programming, London, 1990, pp. 235–248.
J. Cheriyan and S. N. Maheswari, Analysis of Preflow Push Algorithms for Maximum Network Flow,SIAM J. Comput.,18 (1989), 1057–1086.
A. V. Goldberg, Efficient Graph Algorithms for Sequential and Parallel Computers, Ph.D. thesis MIT/LCS/TR-374, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 1987.
A. V. Goldberg and R. E. Tarjan, Finding Minimum-Cost Circulations by Successive Approximations, Technical Report MIT/LCS/TM-333, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 1987.
A. V. Goldberg and R. E. Tarjan, A New Approach to the Maximum Flow Problem,J. Assoc. Comput. Mack.,35 (1988), 921–940.
A. V. Goldberg, É. Tardos, and R. E. Tarjan, Network Flow Algorithms, Technical Report No. 860, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, 1989.
Author information
Authors and Affiliations
Additional information
Communicated by Harold N. Gabow.
Research performed while the author was a Ph.D. student at Cornell University and was partially supported by the Ministry of Education of the Republic of Turkey through the scholarship program 1416.
Rights and permissions
About this article
Cite this article
Tunçel, L. On the complexity of preflow-push algorithms for maximum-flow problems. Algorithmica 11, 353–359 (1994). https://doi.org/10.1007/BF01187018
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01187018