Abstract
We develop an arsenal of tools for improving the efficiency of parallel algorithms for network-flow problems and apply it to a maximum-flow algorithm of Goldberg, a blocking-flow algorithm of Shiloach and Vishkin, and a maximum-flow algorithm of Ahuja and Orlin. Depending on the exact model of computation and the time available for the computation, we achieve a polylogarithmic reduction in the time-processor product. In particular, this leads to the first parallel implementations with optimal speedup of the corresponding sequential algorithms.
Part of the research was carried out while this author was with the Max-Planck-Institut für Informatik.
Supported by the ESPRIT Basic Research Actions Program of the EU under contract No. 7141 (project ALCOM II).
Preview
Unable to display preview. Download preview PDF.
References
R. K. Ahuja and J. B. Orlin, A fast and simple algorithm for the maximum flow problem, Oper. Res. 37 (1989), pp. 748–759.
R. K. Ahuja, J. B. Orlin, and R. E. Tarjan, Improved time bounds for the maximum flow problem, SIAM J. Comput. 18 (1989), pp. 939–954.
R. K. Ahuja, J. B. Orlin, C. Stein, and R. E. Tarjan, Improved algorithms for bipartite network flow, SIAM J. Comput. 23 (1994), pp. 906–933.
S. Albers and T. Hagerup, Improved parallel integer sorting without concurrent writing, Tech. Rep. No. MPI-I-94-137, Max-Planck-Institut für Informatik, Saarbrücken, 1994. A preliminary version appeared in Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1992), pp. 463–472.
H. Bast and T. Hagerup, Fast parallel space allocation, estimation and integer sorting, Tech. Rep. No. MPI-I-93-123, Max-Planck-Institut für Informatik, Saarbrücken, 1993. Also Inform, and Comput., to appear.
P. Beame and J. Hastad, Optimal bounds for decision problems on the CRCW PRAM, J. Assoc. Comput. Mach. 36 (1989), pp. 643–670.
P. C. P. Bhatt, K. Diks, T. Hagerup, V. C. Prasad, T. Radzik, and S. Saxena, Improved deterministic parallel integer sorting, Inform. and Comput. 94 (1991), pp. 29–47.
J. Cheriyan and S. N. Maheshwari, Analysis of preflow push algorithms for maximum network flow, SIAM J. Comput. 18 (1989), pp. 1057–1086.
R. Cole and U. Vishkin, Deterministic coin tossing with applications to optimal parallel list ranking, Inform. and Control 70 (1986), pp. 32–53.
E. A. Dinic, Algorithm for solution of a problem of maximum flow in a network with power estimation, Soviet Math. Dokl. 11 (1970), pp. 1277–1280.
A. V. Goldberg, Processor-efficient implementation of a maximum flow algorithm, Inform. Process. Lett. 38 (1991), pp. 179–185.
A. V. Goldberg and R. E. Tarjan, A new approach to the maximum-flow problem, J. Assoc. Comput. Mach. 35 (1988), pp. 921–940.
A. V. Goldberg and R. E. Tarjan, Finding minimum-cost circulations by successive approximation, Math. of Oper. Res. 15 (1990), pp. 430–466.
T. Hagerup, Fast deterministic processor allocation, J. Algorithms 18 (1995), pp. 629–649.
T. Hagerup, K. Mehlhorn, and J. I. Munro, Maintaining discrete probability distributions optimally, in Proc. 20th International Colloquium on Automata, Languages and Programming (ICALP 1993), Springer Lecture Notes in Computer Science, Vol. 700, pp. 253–264.
C. P. Kruskal, L. Rudolph, and M. Snir, Efficient parallel algorithms for graph problems, Algorithmica 5 (1990), pp. 43–64.
W. Paul, U. Vishkin, and H. Wagener, Parallel computation on 2–3 trees, RAIRO Theoret. Inform. 17 (1983), pp. 397–404.
Y. Shiloach and U. Vishkin, An O(n 2 log n) parallel MAX-FLOW algorithm, J. Algorithms 3 (1982), pp. 128–146.
U. Vishkin, A parallel blocking flow algorithm for acyclic networks, J. Algorithms 13 (1992), pp. 489–501.
R. A. Wagner and Y. Han, Parallel algorithms for bucket sorting and the data dependent prefix problem, in Proc. International Conference on Parallel Processing (1986), pp. 924–930.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dedorath, J., Gergov, J., Hagerup, T. (1995). More efficient parallel flow algorithms. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015428
Download citation
DOI: https://doi.org/10.1007/BFb0015428
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60573-7
Online ISBN: 978-3-540-47766-2
eBook Packages: Springer Book Archive