A faster capacity scaling algorithm for minimum cost submodular flow

Mathematical Programming, Series B

Volumn 92, Issue 1, 2002, Pages 119-139

  Fleischer, Lisa ^a   Iwata, Satoru ^b   McCormick, S Thomas ^c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF TOKYO   (Japan)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Network flow; Scaling algorithm; Submodular function

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; GRAPH THEORY; OPTIMIZATION; POLYNOMIAL APPROXIMATION; SUBROUTINES;

NETWORK FLOW; RESIDUAL CAPACITY; SCALING ALGORITHM; SUBMODULAR FUNCTION;

COMPUTATIONAL METHODS;

EID: 0038768432     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100253     Document Type: Article

References (35)

1. Birkhoff, G. (1967): Lattice Theory. Amer. Math. Soc.
2. Cunningham, W.H., Frank, A. (1985): A primal-dual algorithm for submodular flows. Math. Oper. Res. 10, 251-262
3. Edmonds, J. (1970): Submodular functions, matroids, and certain polyhedra. In: Guy, R., Hanani, H., Sauer, N., Schönheim, J., eds., Combinatorial Structures and Their Applications. Gordon and Breach, pp. 69-87
4. Edmonds, J., Giles, R. (1977): A min-max relation for submodular functions on graphs. Ann. Discrete Math, 1, 185-204
5. Edmonds, J., Karp, R.M. (1972): Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19, 248-264
6. Ervolina, T.R., McCormick, S.T. (1993): Two strongly polynomial cut canceling algorithms for minimum cost network flow. Discrete Appl. Math. 46, 133-165
7. Fleischer, L., Iwata, S. (2000): Improved algorithms for submodular function minimization and submodular flow. Proceedings of the 32th Annual ACM Symposium on Theory of Computing, 107-116
8. Frank, A. (1984): Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory, Ser. B 36, 221-239
9. Frank, A., Tardos, É. (1987): An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7, 49-65
10. Frank, A., Tardos, É. (1988): Generalized polymatroids and submodular flows. Math. Program. 42, 489-563
11. Fujishige, S. (1978): Algorithms for solving the independent-flow problems. J. Oper. Res. Soc. Japan 21, 189-204
12. Fujishige, S. (1984): Structures of polyhedra determined by submodular functions on crossing families. Math. Programming 29, 125-141
13. Fujishige, S. (1986): A capacity-rounding algorithm for the minimum cost circulation problem - A dual framework of the Tardos algorithm. Math. Programming 35, 298-308
14. Fujishige, S. (1991): Submodular Functions and Optimization. North-Holland
15. Fujishige, S., Iwata, S. (2000): Algorithms for submodular flows. IEICE Trans. Inform. Syst. E83-D, 322-329.
16. Fujishige, S., Röck, H., Zimmermann, U. (1989): A strongly polynomial algorithm for minimum cost submodular flow problems. Math. Oper. Res. 14, 60-69
17. Fujishige, S., Tomizawa, N. (1983): A note on submodular functions on distributive lattices. J. Oper. Res. Soc. Japan 26, 309-318
18. Fujishige, S., Zhang, X. (1992): New algorithms for the intersection problem of submodular systems. Japan J. Indust. Appl. Math. 9, 369-382
19. Iwata, S. (1997): A capacity scaling algorithm for convex cost submodular flows. Math. Programming 76, 299-308
20. Iwata, S. (2000): A fully combinatorial algorithm for submodular function minimization. METR 00-09, University of Tokyo, October 2000. To appear in J. Combin. Theory, Ser. B
21. Iwata, S., Fleischer, L., Fujishige, S. (2000): A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions. Proceedings of the 32th Annual ACM Symposium on Theory of Computing, 97-106. To appear in J. ACM
22. Iwata, S., McCormick, S.T., Shigeno, M. (1998): A faster algorithm for minimum cost submodular flows. Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, 167-174. To appear in Combinatorica
23. Iwata, S., McCormick, S.T., Shigeno, M. (1999): A strongly polynomial cut canceling algorithm for the submodular flow problem. Proceedings of the Seventh MPS Conference on Integer Programming and Combinatorial Optimization, 259-272
24. Iwata, S., McCormick, S.T., Shigeno, M. (2000): A fast cost scaling algorithm for submodular flow. Inform. Process. Lett. 74, 123-128
25. Lawler, E.L., Martel, C.U. (1982): Computing maximal polymatroidal network flows. Math. Open Res. 7, 334-347
26. Lucchesi, C.L., Younger, D.H. (1978): A minimax relation for directed graphs. J. London Math. Soc. 17, 369-374
27. McCormick, S.T., Ervolina, T.R. (1994): Computing maximum mean cuts. Discrete Appl. Math. 52, 53-70
28. Naitoh, T., Fujishige, S. (1992): A note on the Frank-Tardos bi-truncation algorithm for crossing-submodular functions. Math. Programming 53, 361-363
29. Radzik, T. (1992): Newton's method for fractional combinatorial optimization. Proceedings of the 33rd IEEE Annual Symposium on Foundations of Computer Science, 659-669.
30. Parametric flows, weighted means of cuts, and fractional combinatorial optimization. Complexity in Numerical Optimization, Pardalos, P., ed., World Scientific, 1993, 351-386
31. Schönsleben, P. (1980): Ganzzahlige Polymatroid-Intersektions Algorithmen. Dissertation, ETH Zürich
32. Schrijver, A. (2000): A combinatorial algorithm minimizing submodular functions in strongly polynomial time. J. Combin. Theory, Ser. B 80, 346-355
33. Shigeno, M., Iwata, S., McCormick, S.T. (2000): Relaxed most negative cycle and most positive cut canceling algorithms for minimum cost flow. Math. Open Res. 25, 76-104
34. Tardos, E. (1985): A strongly polynomial minimum cost circulation algorithm. Combinatorica 5, 247-256
35. Tardos, É., Tovey, C.A., Trick, M.A. (1986): Layered augmenting path algorithms. Math. Oper. Res. 11, 362-370