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An O(nm)-Time Network Simplex Algorithm for the Shortest Path Problem

Author

Listed:
  • Donald Goldfarb

    (Columbia University, New York, New York)

  • Zhiying Jin

    (GTE Laboratories, Inc., Waltham, Massachusetts)

Abstract

We present an O ( nm )-time network simplex algorithm for finding a tree of shortest paths from a given node to all other nodes in a network of n nodes and m directed arcs or finding a directed cycle of negative length. The worst-case running time of this algorithm is as fast as that proved for any strongly polynomial algorithm and faster than that proved for any previously proposed simplex algorithm for this problem. We also show that this algorithm can be implemented in O ( nlogn ) time using O (( m / logn ) + n ) exclusive read–exclusive write processors of a parallel random access machine.

Suggested Citation

  • Donald Goldfarb & Zhiying Jin, 1999. "An O(nm)-Time Network Simplex Algorithm for the Shortest Path Problem," Operations Research, INFORMS, vol. 47(3), pages 445-448, June.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:3:p:445-448
    DOI: 10.1287/opre.47.3.445
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    References listed on IDEAS

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    1. W. H. Cunningham, 1979. "Theoretical Properties of the Network Simplex Method," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 196-208, May.
    2. Donald Goldfarb & Jianxiu Hao & Sheng-Roan Kai, 1990. "Efficient Shortest Path Simplex Algorithms," Operations Research, INFORMS, vol. 38(4), pages 624-628, August.
    3. George J. Minty, 1958. "Letter to the Editor---A Variant on the Shortest-Route Problem," Operations Research, INFORMS, vol. 6(6), pages 882-883, December.
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    Cited by:

    1. I-Lin Wang & Ellis L. Johnson & Joel S. Sokol, 2005. "A Multiple Pairs Shortest Path Algorithm," Transportation Science, INFORMS, vol. 39(4), pages 465-476, November.

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