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A least-squares minimum-cost network flow algorithm

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  • Balaji Gopalakrishnan
  • Seunghyun Kong
  • Earl Barnes
  • Ellis Johnson
  • Joel Sokol

Abstract

Node-arc incidence matrices in network flow problems exhibit several special least-squares properties. We show how these properties can be leveraged in a least-squares primal-dual algorithm for solving minimum-cost network flow problems quickly. Computational results show that the performance of an upper-bounded version of the least-squares minimum-cost network flow algorithm with a special dual update operation is comparable to CPLEX Network and Dual Optimizers for solving a wide range of minimum-cost network flow problems. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:119-140:10.1007/s10479-011-0858-7
    DOI: 10.1007/s10479-011-0858-7
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    1. C. O. Fong & V. Srinivasan, 1977. "Determining All Nondegenerate Shadow Prices for the Transportation Problem," Transportation Science, INFORMS, vol. 11(3), pages 199-222, August.
    2. 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.
    3. Antonio Frangioni & Antonio Manca, 2006. "A Computational Study of Cost Reoptimization for Min-Cost Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 61-70, 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. Warren B. Powell, 1989. "A Review of Sensitivity Results for Linear Networks and a New Approximation to Reduce the Effects of Degeneracy," Transportation Science, INFORMS, vol. 23(4), pages 231-243, November.
    6. W. H. Cunningham, 1979. "Theoretical Properties of the Network Simplex Method," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 196-208, May.
    7. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
    8. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
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