IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v95y1997i3d10.1023_a1022613603828.html
   My bibliography  Save this article

Efficient Parallel Algorithms for the Minimum Cost Flow Problem

Author

Listed:
  • P. Beraldi

    (Università della Calabria)

  • F. Guerriero

    (Università della Calabria)

  • R. Musmanno

    (Università della Calabria)

Abstract

In this paper, we propose efficient parallel implementations of the auction/sequential shortest path and the ∈-relaxation algorithms for solving the linear minimum cost flow problem. In the parallel auction algorithm, several augmenting paths can be found simultaneously, each of them starting from a different node with positive surplus. Convergence results of an asynchronous version of the algorithm are also given. For the ∈-relaxation method, there exist already parallel versions implemented on CM-5 and CM-2; our implementation is the first on a shared memory multiprocessor. We have obtained significant speedup values for the algorithms considered; it turns out that our implementations are effective and efficient.

Suggested Citation

  • P. Beraldi & F. Guerriero & R. Musmanno, 1997. "Efficient Parallel Algorithms for the Minimum Cost Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 501-530, December.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:3:d:10.1023_a:1022613603828
    DOI: 10.1023/A:1022613603828
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022613603828
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022613603828?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richard S. Barr & Betty L. Hickman, 1994. "Parallel Simplex for Large Pure Network Problems: Computational Testing and Sources of Speedup," Operations Research, INFORMS, vol. 42(1), pages 65-80, February.
    2. Li, Xiaoye & Zenios, Stavros A., 1994. "Data-level parallel solution of min-cost network flow problems using [epsilon]-relaxations," European Journal of Operational Research, Elsevier, vol. 79(3), pages 474-488, December.
    3. Dimitri P. Bertsekas & Paul Tseng, 1988. "Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems," Operations Research, INFORMS, vol. 36(1), pages 93-114, February.
    4. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    5. Fred Glover & D. Karney & D. Klingman & A. Napier, 1974. "A Computation Study on Start Procedures, Basis Change Criteria, and Solution Algorithms for Transportation Problems," Management Science, INFORMS, vol. 20(5), pages 793-813, January.
    6. Ellis L. Johnson, 1966. "Networks and Basic Solutions," Operations Research, INFORMS, vol. 14(4), pages 619-623, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    2. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    3. Festa, P. & Guerriero, F. & Laganà, D. & Musmanno, R., 2013. "Solving the shortest path tour problem," European Journal of Operational Research, Elsevier, vol. 230(3), pages 464-474.
    4. R. Fourer & H. Gassmann & J. Ma & R. Martin, 2009. "An XML-based schema for stochastic programs," Annals of Operations Research, Springer, vol. 166(1), pages 313-337, February.
    5. Mongeau, Marcel & Sartenaer, Annick, 1995. "Automatic decrease of the penalty parameter in exact penalty function methods," European Journal of Operational Research, Elsevier, vol. 83(3), pages 686-699, June.
    6. Moreno, Alfredo & Munari, Pedro & Alem, Douglas, 2019. "A branch-and-Benders-cut algorithm for the Crew Scheduling and Routing Problem in road restoration," European Journal of Operational Research, Elsevier, vol. 275(1), pages 16-34.
    7. Dayal Madhukar & Verma, Sanjay, 2015. "Multi-processor Exact Procedures for Regular Measures of the Multi-mode RCPSP," IIMA Working Papers WP2015-03-25, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Ahuja, Ravindra K., 1956- & Orlin, James B., 1953-, 1992. "Use of representative operation counts in computational testings of algorithms," Working papers 3459-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. Sharma, R. R. K. & Sharma, K. D., 2000. "A new dual based procedure for the transportation problem," European Journal of Operational Research, Elsevier, vol. 122(3), pages 611-624, May.
    10. X-Y Li & Y P Aneja & F Baki, 2010. "An ant colony optimization metaheuristic for single-path multicommodity network flow problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1340-1355, September.
    11. Herminia Calvete & Lourdes del-Pozo & José Iranzo, 2012. "Algorithms for the quickest path problem and the reliable quickest path problem," Computational Management Science, Springer, vol. 9(2), pages 255-272, May.
    12. Avinash Unnikrishnan & Varunraj Valsaraj & Steven Waller, 2009. "Stochastic and Dynamic Shipper Carrier Network Design Problem," Networks and Spatial Economics, Springer, vol. 9(4), pages 525-550, December.
    13. Francesca Guerriero & Roberto Musmanno & Valerio Lacagnina & Antonio Pecorella, 2001. "A Class of Label-Correcting Methods for the K Shortest Paths Problem," Operations Research, INFORMS, vol. 49(3), pages 423-429, June.
    14. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    15. Mingue SUn, 2010. "A Branch-and-Bound Algorithm for Representative Integer Efficient Solutions in Multiple Objective Network Programming Problems," Working Papers 0007, College of Business, University of Texas at San Antonio.
    16. Marins, Fernando A. S. & Senne, Edson L. F. & Darby-Dowman, Ken & Machado, Arlene F. & Perin, Clovis, 1997. "Algorithms for network piecewise-linear programs: A comparative study," European Journal of Operational Research, Elsevier, vol. 97(1), pages 183-199, February.
    17. Prahalad Venkateshan & Kamlesh Mathur & Ronald H. Ballou, 2008. "An efficient generalized network-simplex-based algorithm for manufacturing network flows," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 315-341, May.
    18. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    19. Gregory M. Kellar & George G. Polak & Xinhui Zhang, 2016. "Synchronization, cross-docking, and decoupling in supply chain networks," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2585-2599, May.
    20. F. Guerriero & P. Tseng, 2002. "Implementation and Test of Auction Methods for Solving Generalized Network Flow Problems with Separable Convex Cost," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 113-144, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:95:y:1997:i:3:d:10.1023_a:1022613603828. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.