An Efficient Implementation of a Scaling Minimum-Cost Flow Algorithm

Journal of Algorithms

Volumn 22, Issue 1, 1997, Pages 1-29

  Goldberg, Andrew V ^a  

^a NEC LABORATORIES AMERICA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001852170     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.1995.0805     Document Type: Article

References (36)

1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network flows, in "Optimization. Handbooks in Operations Research and Management Science" (G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd, Eds.), Vol. 1, pp. 211-369, North-Holland, Amsterdam, 1989.
2. R. J. Anderson and J. C. Setubal, Goldberg's algorithm for the maximum flow in perspective: A computational study, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. C. Johnson and C. C. McGeoch, Eds.), pp. 1-18, AMS, Providence, 1993.
3. D. P. Bertsekas, "Distributed Asynchronous Relaxation Methods for Linear Network Flow Problems," Technical Report LIDS-P-1986, Laboratory for Decision Systems, M.I.T., Sept. 1986. (Revised, Nov. 1986).
4. D. P. Bertsekas and P. Tseng, Relaxation methods for minimum cost ordinary and generalized network flow problems, Oper. Res. 36 (1988), 93-114.
5. R. G. Bland, J. Cheriyan, D. J. Jensen, and L. Ladańyi, An empirical study of min cost flow algorithms, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. S. Johnson and C. C. McGeoch, Eds.), pp. 119-158, AMS, Providence, 1993.
6. R. G. Bland and D. L. Jensen, On the computational behavior of a polynomial-time network flow algorithm, Math. Prog. 54 (1992), 1-41.
7. G. Bradley, G. Brown, and G. Graves, Design and implementation of large scale transportation algorithms, Management Sci. 21 (1977), 1-38.
8. M. D. Chang and C. J. Chen, An improved primal simplex variant for pure processing networks, ACM Trans. Math. Software 15 (1989), 64-78.
9. B. V. Cherkassky, Personal communication, 1992.
10. B. V. Cherkassky and A. V. Goldberg, "On Implementing Push-Relabel Method for the Maximum Flow Problem," Technical Report STAN-CS-94-1523, Department of Computer Science, Stanford University, 1994.
11. U. Derigs and W. Meier, Implementing Goldberg's max-flow algorithm - A computational investigation, ZOR - Methods Models Oper. Res. 33 (1989), 383-403.
12. U. Derigs and W. Meier, Goldrmf/Goldnet-max-flow program. Europ. J. Oper Res. 46 (1990), 260.
13. R. B. Dial, Algorithm 360: Shortest path forest with topological ordering, Commun. ACM 12 (1969), 632-633.
14. L. R. Ford, Jr. and D. R. Fulkerson, "Flows in Networks," Princeton Univ. Press, Princeton, NJ, 1962.
15. S. Fujishige, K. Iwano, J. Nakano, and S. Tezuka, A speculative contraction method for the minimum cost flows: Toward a practical algorithm, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. S. Johnson and C. C. McGeoch, Eds.), pp. 219-246, AMS, Providence, 1993.
16. F. Glover, D. Karney, and D. Klingman, Implementation and computational comparison of primal, dual, and primal-dual computer codes for minimum cost network flow problem, Networks 4 (1974), 191-212.
17. A. V. Goldberg, "A New Max-Flow Algorithm," Technical Report MIT/LCS/TM-291, Laboratory for Computer Science, M.I.T., 1985.
18. A. V. Goldberg, "Efficient Graph Algorithms for Sequential and Parallel Computers," Ph.D. thesis, M.I.T., January 1987. (Also available as Technical Report TR-374, Laboratory for Computer Science, M.I.T., 1987.)
19. A. V. Goldberg, Scaling algorithms for the shortest paths problem, SIAM J. Comput. 24 (1995), 494-504.
20. A. V. Goldberg and R. Kennedy, "An Efficient Cost Scaling Algorithm for the Assignment Problem," Technical Report STAN-CS-93-1481, Department of Computer Science, Stanford University, 1993.
21. A. V. Goldberg and M. Kharitonov, On implementing scaling push-relabel algorithms for the minimum-cost flow problem, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. S. Johnson and C. C. McGeoch, Eds.), pp. 157-198, AMS, Providence, 1993.
22. A. V. Goldberg, É. Tardos, and R. E. Tarjan, Network flow algorithms, in "Flows, Paths, and VLSI Layout" (B. Korte, L. Lovász, H. J. Prömel, and A. Schrijver, Eds.), pp. 101-164, Springer-Verlag, Berlin, 1990.
23. A. V. Goldberg and R. E. Tarjan, A new approach to the maximum flow problem, J. Assoc. Comput. Mach. 35 (1988), 921-940.
24. A. V. Goldberg and R. E. Tarjan, Finding minimum-cost circulations by successive approximation, Math. Oper Res. 15 (1990), 430-466.
25. M. D. Grigoriadis, An efficient implementation of the network simplex method, Math. Prog. Study 26 (1986), 83-111.
26. D. S. Johnson and C. C. McGeoch, "Network Flows and Matching: First DIMACS Implementation Challenge," AMS, Providence, 1993.
27. A. Joshi, A. S. Goldstein, and P. M. Vaidya, A fast implementation of a path-following algorithm for maximizing a linear function over a network polytope, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. S. Johnson and C. C. McGeoch, Eds.), pp. 267-298, AMS, Providence, 1993.
28. N. K. Karmarkar and K. G. Ramakrishnan, Computational results of an interior point algorithm for large scale linear programming, Math. Prog. 52 (1991), 555-586.
29. J. L. Kennington and R. V. Helgason, "Algorithms for Network Programming," Wiley, New York, 1980.
30. D. Klingman, A. Napier, and J. Stutz, A program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems, Management Sci. 20 (1974), 814-821.
31. I. Maros, Performance Evaluation of MINET minimum cost netflow solver, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. S. Johnson and C. C. McGeoch, Eds.), pp. 199-217, AMS, Providence, 1993.
32. J. Mulvey, Pivot strategies for primal-simplex network codes, J. Assoc. Comput. Mach. (1978), 266-270.
33. Q. C. Nguyen and V. Venkateswaran, Implementations of Goldberg-Tarjan maximum flow algorithm, in "Network Flows and Matching: First DIMACS Implementation Challenge (D. S. Johnson and C. C. McGeoch, Eds.), pp. 19-42, AMS, Providence, 1993.
34. M. G. C. Resende and G. Veiga, An efficient implementation of a network interior point method, in "Network Flows and Matching: First DIMACS Implementation Challenge" (D. S. Johnson and C. C. McGeoch, Eds.), pp. 299-348, AMS, Providence, 1993.
35. H. Röck, Scaling techniques for minimal cost network flows, in "Discrete Structures and Algorithms" (U. Pape, Eds.), pp. 181-191, Carl Hansen, Munich, 1980.
36. É. Tardos, A strongly polynomial minimum cost circulation algorithm, Combinatorica 5(3) (1985), 247-255.