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Efficient Shortest Path Simplex Algorithms

Author

Listed:
  • Donald Goldfarb

    (Columbia University, New York, New York)

  • Jianxiu Hao

    (GTE Laboratories, Waltham, Massachusetts)

  • Sheng-Roan Kai

    (GTE Laboratories, Waltham, Massachusetts)

Abstract

We consider the specialization of the primal simplex algorithm to the problem of finding a tree of directed shortest paths from a given node to all other nodes in a network of n nodes or finding a directed cycle of negative length. Two efficient variants of this shortest path simplex algorithm are analyzed and shown to require at most ( n − 1)( n − 2)/2 pivots and O ( n 3 ) time.

Suggested Citation

  • Donald Goldfarb & Jianxiu Hao & Sheng-Roan Kai, 1990. "Efficient Shortest Path Simplex Algorithms," Operations Research, INFORMS, vol. 38(4), pages 624-628, August.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:4:p:624-628
    DOI: 10.1287/opre.38.4.624
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    Citations

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    Cited by:

    1. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    2. 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.
    3. 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.
    4. Orlin, James B., 1953-, 1995. "A polynomial time primal network simplex algorithm for minimum cost flows," Working papers 3834-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    5. Sedeño-Noda, Antonio & González-Martín, Carlos, 2010. "On the K shortest path trees problem," European Journal of Operational Research, Elsevier, vol. 202(3), pages 628-635, May.

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