论文信息 - Generalizing the all-pairs min cut problem

Generalizing the all-pairs min cut problem

The all-pairs min cut (APMC) problem on a nonnegative edge-weighted graph is to find, for each pair of nodes, a min cut that separates the pair. Gomory and Hu (1961) presented a structural characterization of collections of cuts that solve the APMC problem. We show how the APMC problem can be generalized to matroids and we present several theorems that characterize the structure of solutions to this more general problem. The result of Gomory and Hu is a special case of one of these theorems. In particular, we find that the APMC problem is a matroid optimization problem.

David Hartvigsen | David Hartvigsen

[1] L. E. Trotter,et al. On the Generality of Multi-Terminal Flow Theory , 1977 .

[2] S. Vajda,et al. Integer Programming and Network Flows , 1970 .

[3] Harvey J. Greenberg,et al. Advanced techniques in the practice of operations research , 1982 .

[4] T. Gallai. Über reguläre Kettengruppen , 1959 .

[5] Klaus Truemper,et al. A decomposition of the matroids with the max-flow min-cut property , 1986, Discret. Appl. Math..

[6] T. C. Hu,et al. Multi-Terminal Network Flows , 1961 .

[7] Paul D. Seymour,et al. The matroids with the max-flow min-cut property , 1977, J. Comb. Theory B.

[8] D. R. Fulkerson. NETWORKS, FRAMES, BLOCKING SYSTEMS , 1967 .

[9] D. R. Fulkerson,et al. Flows in Networks. , 1964 .

[10] Refael Hassin. Solution Bases of Multiterminal Cut Problems , 1988, Math. Oper. Res..

[11] Klaus Truemper,et al. Max-Flow Min-Cut Matroids: Polynomial Testing and Polynomial Algorithms for Maximum Flow and Shortest Routes , 1987, Math. Oper. Res..

[12] Refael Hassin,et al. Multi-terminal maximum flows in node-capacitated networks , 1986 .