Fast cycle canceling algorithms for minimum cost submodular flow

Combinatorica

Volumn 23, Issue 3, 2003, Pages 503-525

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

^a UNIVERSITY OF TOKYO   (Japan)

^b UNIVERSITY OF TSUKUBA   (Japan)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346328412     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-003-0030-3     Document Type: Article

References (37)

1. R. K. AHUJA, T. L. MAGNANTI, and J. B. ORLIN: Network Flows - Theory, Algorithms, and Applications, Prentice Hall (1993).
2. W. CUI and S. FUJISHIGE: A primal algorithm for the submodular flow problem with minimum-mean cycle selection, J. Oper. Res. Soc. Japan, 31 (1988), 431-440.
3. W. H. CUNNINGHAM and A. FRANK: A primal-dual algorithm for submodular flows, Math. Oper. Res., 10 (1985), 251-262.
4. J. EDMONDS and R. GILES: A min-max relation for submodular functions on graphs, Ann. Discrete Math., 1 (1977), 185-204.
5. J. EDMONDS and R. M. KARP: Theoretical improvements in algorithmic efficiency for network flow problems, J. ACM, 19 (1972), 248-264.
6. L. FLEISCHER, S. IWATA, and S. T. MCCORMICK: A faster capacity-scaling algorithm for minimum cost submodular flow, Math. Programming, 92 (2002), 119-139.
7. A. FRANK: Finding feasible vectors of Edmonds-Giles polyhedra, J. Combinatorial Theory, Ser. B, 36 (1984), 221-239.
8. A. FRANK and É. TARDOS: An application of simultaneous Diophantine approximation in combinatorial optimization, Combinatorica, 7 (1987), 49-65.
9. A. FRANK and É. TARDOS: Generalized polymatroids and submodular flows, Math. Programming, 42 (1988), 489-563.
10. S. FUJISHIGE: Algorithms for solving the independent-flow problems, J. Oper. Res. Soc. Japan, 21 (1978), 189-204.
11. S. FUJISHIGE: Submodular Functions and Optimization, North-Holland, 1991.
12. S. FUJISHIGE, H. RÖCK, and U. ZIMMERMANN: A strongly polynomial algorithm for minimum cost submodular flow problems, Math. Oper. Res., 14 (1989), 60-69.
13. S. FUJISHIGE and X. ZHANG: New algorithms for the intersection problem of submodular systems, Japan J. Indust. Appl. Math., 9 (1992), 369-382.
14. A. V. GOLDBERG: Scaling algorithms for the shortest paths problem, SIAM J. Comput., 24 (1995), 494-504.
15. A. V. GOLDBERG and R. E. TARJAN: Finding minimum-cost circulations by canceling negative cycles, J. ACM, 36 (1989), 873-886.
16. A. V. GOLDBERG and R. E. TARJAN: Finding minimum-cost circulations by successive approximation, Math. Oper. Res., 15 (1990), 430-466.
17. M. GRÖTSCHEL, L. LOVÁSZ, and A. SCHRIJVER: Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, 1988.
18. R. HASSIN: Minimum cost flow with set-constraints, Networks, 12 (1982), 1-21.
19. D. S. HOCHBAUM and J. G. SHANTHIKUMAR: Convex separable optimization is not much harder than linear optimization, J. ACM, 37 (1990), 843-862.
20. S. IWATA: A capacity scaling algorithm for convex cost submodular flows, Math. Programming, 76 (1997), 299-308.
21. S. IWATA, L. FLEISCHER, AND S. FUJISHIGE: A combinatorial strongly polynomial-time algorithm for minimizing submodular functions, J. ACM, 48 (2001), 761-777.
22. S. IWATA, S. T. MCCORMICK, and M. SHIGENO: A faster algorithm for minimum cost submodular flows, Proceedings of the Ninth Annual ACM/SIAM Symposium on Discrete Algorithms (1998), 167-174.
23. S. IWATA, S. T. MCCORMICK, and M. SHIGENO: A strongly polynomial cut canceling algorithm for the submodular flow problem, Proceedings of the Seventh MPS Conference on Integer Programming and Combinatorial Optimization (1999), G. Cornuéjols, R. E. Burkard, and G. J. Woeginger, eds., 259-272.
24. S. IWATA, S. T. MCCORMICK, and M. SHIGENO: A fast cost scaling algorithm for submodular flow, Inform. Process. Lett., 74 (2000), 123-128.
25. S. IWATA, S. T. MCCORMICK, and M. SHIGENO: A relaxed cycle-canceling approach to separable convex optimization in unimodular linear spaces, in preparation.
26. R. M. KARP: A characterization of the minimum cycle mean in a digraph, Discrete Math., 23 (1978), 309-311.
27. A. V. KARZANOV and S. T. MCCORMICK: Polynomial methods for separable convex optimization in totally unimodular linear spaces with applications to circulations and co-circulations in networks, SIAM J. Comput., 26 (1997), 1245-1275.
28. E. L. LAWLER and C. U. MARTEL: Computing maximal polymatroidal network flows, Math. Oper. Res., 7 (1982), 334-347.
29. T. NAITOH and S. FUJISHIGE: A note on the Frank-Tardos bitruncation algorithm for crossing-submodular functions. Math. Programming, 53 (1992), 361-363.
30. R. T. ROCKAFELLAR: Network Flows and Monotropic Optimization. Wiley Interscience, New York, NY (1984).
31. P. SCHÖNSLEBEN: Ganzzahlige Polymatroid-Intersektions-Algorithmen, ETH Zürich (1980).
32. A. SCHRIJVER: A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combinatorial Theory, Ser. B, 80 (2000), 346-355.
33. M. SHIGENO, S. IWATA, and S. T. MCCORMICK: Relaxed most negative cycle and most positive cut canceling algorithms for minimum cost flow, Math. Oper. Res., 25 (2000), 76-104.
34. É. TARDOS: A strongly polynomial minimum cost circulation algorithm, Combinatorica, 5 (1985), 247-256.
35. É. TARDOS, C. A. TOVEY, and M. A. TRICK: Layered augmenting path algorithms, Math. Oper. Res., 11 (1986), 362-370.
36. C. WALLACHER and U. ZIMMERMANN: A polynomial cycle canceling algorithm for submodular flows, Math. Programming, 86 (1999), 1-15.
37. U. ZIMMERMANN: Negative circuits for flows and submodular flows, Discrete Appl. Math., 36 (1992), 179-189.