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A Fast and Simple Algorithm for the Maximum Flow Problem

Author

Listed:
  • R. K. Ahuja

    (Massachusetts Institute of Technology, Cambridge, Massachusetts and Indian Institute of Technology, Kanpur, India)

  • James B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We present a simple sequential algorithm for the maximum flow problem on a network with n nodes, m arcs, and integer arc capacities bounded by U . Under the practical assumption that U is polynomially bounded in n , our algorithm runs in time O ( nm + n 2 log n ). This result improves the previous best bound of O ( nm log( n 2 / m )), obtained by Goldberg and Tarjan, by a factor of log n for networks that are both nonsparse and nondense without using any complex data structures. We also describe a parallel implementation of the algorithm that runs in O ( n 2 log U log p ) time in the PRAM model with EREW and uses only p processors where p = ⌈ m / n ⌉.

Suggested Citation

  • R. K. Ahuja & James B. Orlin, 1989. "A Fast and Simple Algorithm for the Maximum Flow Problem," Operations Research, INFORMS, vol. 37(5), pages 748-759, October.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:5:p:748-759
    DOI: 10.1287/opre.37.5.748
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    Citations

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    Cited by:

    1. Antonio Sedeño‐Noda & Carlos González‐Martín, 2000. "A O(nm log(U/n)) time maximum flow algorithm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(6), pages 511-520, September.
    2. Gary R. Waissi, 1993. "A new polynomial algorithm for maximum value flow with an efficient parallel implementation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 393-414, April.
    3. Ahuja, Ravindra K. & Kodialam, Murali & Mishra, Ajay K. & Orlin, James B., 1997. "Computational investigations of maximum flow algorithms," European Journal of Operational Research, Elsevier, vol. 97(3), pages 509-542, March.
    4. Huynh Tuong, Nguyen & Soukhal, Ameur, 2010. "Due dates assignment and JIT scheduling with equal-size jobs," European Journal of Operational Research, Elsevier, vol. 205(2), pages 280-289, September.
    5. Ahuja, Ravindra K., 1956-, 1995. "Computational investigations of maximum flow algorithms," Working papers 3811-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Dorit S. Hochbaum & Anna Chen, 2000. "Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem," Operations Research, INFORMS, vol. 48(6), pages 894-914, December.
    7. E. M. U. S. B. Ekanayake & W. B. Daundasekara & S. P. C. Perera, 2022. "New Approach to Obtain the Maximum Flow in a Network and Optimal Solution for the Transportation Problems," Modern Applied Science, Canadian Center of Science and Education, vol. 16(1), pages 1-30, February.
    8. Ravindra K. Ahuja & James B. Orlin, 1991. "Distance‐directed augmenting path algorithms for maximum flow and parametric maximum flow problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 413-430, June.

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