Fast cost scaling algorithm for submodular flow

Information Processing Letters

Volumn 74, Issue 3, 2000, Pages 123-128

  Iwata, Satoru ^a   McCormick, S Thomas ^b   Shigeno, Maiko ^c  

^a OSAKA UNIVERSITY   (Japan)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

COMBINATORIAL OPTIMIZATION; SUBMODULAR FLOW PROBLEM;

COMPUTATIONAL COMPLEXITY;

EID: 0033734918     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0190(00)00052-1     Document Type: Article

References (35)

1. Ahuja R.K., Goldberg A.V., Orlin J.B., Tarjan R.E. Finding minimum-cost flows by double scaling. Math. Programming. Vol. 53:1992;243-266.
2. Barahona F., Cunningham W.H. A submodular network simplex method. Math. Programming Stud. Vol. 22:1984;9-31.
3. Bland R.G., Jensen D.L. On the computational behavior of a polynomial-time network flow algorithm. Math. Programming. Vol. 54:1992;1-39.
4. Chung K., Tcha D. A dual algorithm for submodular flow problems. Oper. Res. Lett. Vol. 10:1991;489-495.
5. Cui W., Fujishige S. A primal algorithm for the submodular flow problem with minimum-mean cycle selection. J. Oper. Res. Soc. Japan. Vol. 31:1988;431-440.
6. Cunningham W.H., Frank A. A primal-dual algorithm for submodular flows. Math. Oper. Res. Vol. 10:1985;251-262.
7. Dinic E.A. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl. Vol. 11:1970;1277-1280.
8. Edmonds J., Giles R. A min-max relation for submodular functions on graphs. Ann. Discrete Math. Vol. 1:1977;185-204.
9. Fleischer L., Iwata S., McCormick S.T. A faster capacity scaling algorithm for minimum cost submodular flow. Research Report 99-08 Discrete Mathematics and Systems Science. 1999;Osaka University.
10. Frank A. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory. Vol. B 36:1984;221-239.
11. Frank A., Tardos É. An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica. Vol. 7:1987;49-65.
12. Frank A., Tardos É. Generalized polymatroids and submodular flows. Math. Programming. Vol. 42:1988;489-563.
13. Fujishige S. Algorithms for solving the independent-flow problems. J. Oper. Res. Soc. Japan. Vol. 21:1978;189-204.
14. Fujishige S. An out-of-kilter method for submodular flows. Discrete Appl. Math. Vol. 17:1987;3-16.
15. Fujishige S. Submodular Functions and Optimization. 1991;North-Holland, Amsterdam.
16. Fujishige S., Röck H., Zimmermann U. A strongly polynomial algorithm for minimum cost submodular flow problems. Math. Oper. Res. Vol. 14:1989;60-69.
17. Fujishige S., Zhang X. New algorithms for the intersection problem of submodular systems. Japan J. Indust. Appl. Math. Vol. 9:1992;369-382.
18. Gabow H. Scaling algorithms for network problems. J. Comput. Sys. Sci. Vol. 35:1985;148-168.
19. Goldberg A.V., Tarjan R.E. A new approach to the maximum flow problem. J. ACM. Vol. 35:1988;921-940.
20. Goldberg A.V., Tarjan R.E. Finding minimum-cost circulations by successive approximation. Math. Oper. Res. Vol. 15:1990;430-466.
21. Grötschel M., Lovász L., Schrijver A. Geometric Algorithms and Combinatorial Optimization. 1988;Springer, Berlin.
22. Hassin R. Minimum cost flow with set-constraints. Networks. Vol. 12:1982;1-21.
23. Iwata S. A capacity scaling algorithm for convex cost submodular flows. Math. Programming. Vol. 76:1997;299-308.
24. Iwata S., Fleischer L., Fujishige S. A strongly polynomial-time algorithm for minimizing submodular functions. Research Report 99-07 Discrete Mathematics and Systems Science. 1999;Osaka University.
25. Iwata S., McCormick S.T., Shigeno M. A faster algorithm for minimum cost submodular flows. Proc. 9th ACM/SIAM Symposium on Discrete Algorithms. 1998;167-174.
26. Iwata S., McCormick S.T., Shigeno M. A strongly polynomial cut canceling algorithm for the submodular flow problem. Proc. 7th MPS Conference on Integer Programming and Combinatorial Optimization. 1998;259-272.
27. Lawler E.L., Martel C.U. Computing maximal polymatroidal network flows. Math. Oper. Res. Vol. 7:1982;334-347.
28. McCormick S.T., Ervolina T.R. Canceling most helpful total submodular cuts for submodular flow. Proc. 3rd MPS Conference on Integer Programming and Combinatorial Optimization. 1993;343-353.
29. Röck H. Scaling techniques for minimum cost network flows. Pape U. Discrete Structures and Algorithms, Hanser. 1980;181-191.
30. Schönsleben P. Ganzzahlige Polymatroid-Intersektions-Algorithmen. 1980;ETH, Zürich.
31. A. Schrijver, A combinatorial algorithm minimizing submodular functions in strongly polynomial time, Manuscript, CWI University of Amsterdam.
32. Tardos É., Tovey C.A., Trick M.A. Layered augmenting path algorithms. Math. Oper. Res. Vol. 11:1986;362-370.
33. Wallacher C., Zimmermann U. A polynomial cycle canceling algorithm for submodular flows. Math. Programming. Vol. 86:1999;1-15.
34. Zimmermann U. Minimization on submodular flows. Discrete Appl. Math. Vol. 4:1982;303-323.
35. Zimmermann U. Negative circuits for flows and submodular flows. Discrete Appl. Math. Vol. 36:1992;179-189.