对最大流算法历史文献的一个调研
Table: Polynomial algorithms for the max flow problem
| No | Duo to | Year | Running Time; |
|---|---|---|---|
| 1 | Ford & Fulkerson [1] | 1956 | (O(nmU)) |
| 2 | Edmonds and Karp [2] | 1972 | (O(nm^2)) |
| 3 | Dinic [3] | 1970 | (O(n^2m)) |
| 4 | Karzanov [4] | 1974 | (O(n^3)) |
| 5 | Cherkasky [5] | 1977 | (O(n^2sqrt{m})) |
| 6 | Malhotra, Kumar & Maheshwari [6] | 1977 | (O(n^3)) |
| 7 | Galil [7] | 1980 | (O(n^(5/3)m^(2/3))) |
| 8 | Galil & Naaman [8] | 1980 | (O(nmlog^2n)) |
| 9 | Sleator & Tarjan [9] | 1983 | (O(nmlogn)) |
| 10 | Gabow [10] | 1985 | (O(nmlogU)) |
| 11 | Goldberg & Tarjan [11] | 1988 | (O(nmlog(n^2/m))) |
| 12 | Ahuja & Orlin [12] | 1989 | (O(nm + n^2logU)) |
| 13 | Ahuja, Orlin & Tarjan [13] | 1989 | (O(nmlog(nsqrt{U}/(m + 2))) |
| 14 | King, Rao & Tarjan [14] | 1992 | (O(nm+n^{2+e})) |
| 15 | King, Rao & Tarjan [15] | 1994 | (O(nmlog_{m/nlogn}n)) |
| 16 | Cheriyan, Hagerup & Mehlhorn [16] | 1996 | (O(n^3/logn)) |
| 17 | Goldberg & Rao [17] | 1998 | (O(min{n^(2/3),m^{1/2}}mlog{n2/m}logU)) |
| 18 | Orlin [18] | 2012 | (O(nm)) |
| 19 | Orlin [18] | 2012 | (O(n^2/logn) if m = O(n)) |
- [1] L. R. Ford and D. R. Fulkerson. Maximal flow through a network. Canadian Journal of Mathematics, 8:399-404, 1956.
- [2] J. Edmonds and R. M. Karp. Theoretical improvements in algorithmic eciency for network flow problems. Journal of the ACM, 19:248-264, 1972.
- [3] E. A. Dinic. Algorithm for solution of a problem of maximum flow in networks with power estimation. Soviet Mathematics Doklady, 11:1277{1280, 1970
- [4] A. V. Karzanov. Determining the maximal flow in a network by the method of preflows. Soviet Mathematics Doklady, 15:434-437, 1974.
- [5] B. V. Cherkasky. Algorithm for construction of maximal flow in networks with complexity of (O(V^2sqrt{E})) operations. Mathematical Methods of Solution of Economical Problems, 17:112-125, 1977. (In Russian).
- [6] V. M. Malhotra, P. Kumar, and S. N. Maheshwari. An (O(V^3)) algorithm for fi nding the maximum flows in networks. Information Processing Letters, 7:277-278, 1978.
- [7] Z. Galil. An (O(V^{5/3}E^{2/3})) algorithm for the maximal flow problem. Acta Informatica, 14(3):221-242, 1980.
- [8] Z. Galil and A. Naaman. An (O(VElog^2E)) algorithm for the maximal flow problem. J.Computer and System Sciences, 21:203-217., 1980.
- [9] D. D. Sleator and R. E. Tarjan. A data structure for dynamic trees. J. Computer and System Sciences, 24:362-391, 1983.
- [10] H. N. Gabow. A data structure for dynamic trees. J. Computer and System Sciences, 31:148-168, 1985.
- [11] A. V. Goldberg and R. E. Tarjan. A new approach to the maximum flow problem. Journal of the ACM, 35:921-940, 1988.
- [12] R. K. Ahuja and J. B. Orlin. A fast and simple algorithm for the maximum flow problem. Operations Research, 37:748-759, 1989.
- [13] R. K. Ahuja, J. B. Orlin, and R. E. Tarjan. Improved time bounds for the maximum flow problem. SIAM Journal on Computing, 18:939-954, 1989.
- [14] V. King, S. Rao, and R. Tarjan. A faster deterministic maximum flow algorithm. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 157{164, 1992.
- [15] V. King, S. Rao, and R. Tarjan. A faster deterministic maximum flow algorithm. J. Algorithms, 23:447-474, 1994.
- [16] J. Cheriyan, T. Hagerup, and K. Mehlhorn. An (O(n^3)) time maximum-flow algorithm. SIAM Journal on Computing, 45:1144-1170, 1996.
- [17] A. V. Goldberg and S. Rao. Beyond the flow decomposition barrier. Journal of the ACM, 45:783-797, 1998.
- [18] J. B. Orlin, “Max flows in (o(nm)) time, or better,” in Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, ser. STOC ’13. New York, NY,USA: ACM, 2013, pp. 765–774. [Online]. Available: http://doi.acm.org/10.1145/2488608.2488705