Abstract
The importance of min-max relations to combinatorial optimization was mentioned in Chapter 1. Perhaps the most useful of these is the celebrated max-flow min-cut theorem. Indeed, much of flow theory, and the theory of cuts in graphs, has been built around this theorem. It is not surprising, therefore, that a concerted effort was made to obtain generalizations of this theorem to the case of multiple commodities.
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Notes
N. Garg, V.V. Vazirani, and M. Yannakakis. Approximate max-flow min(multi)cut theorems and their applications. SIAM Journal on Computing, 25: 235–251, 1996.
P. Klein, S. Rao, A. Agrawal, and R. Ravi. An approximate max-flow min-cut relation for undirected multicommodity flow, with applications. Combinatorica, 15: 187–202, 1995.
M. Pinsker. On the complexity of a concentrator. In Proc. 7th Annual Teletraffic Conference, pages 318/1–318/4, 1973.
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© 2003 Springer-Verlag Berlin Heidelberg
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Vazirani, V.V. (2003). Multicut in General Graphs. In: Approximation Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04565-7_20
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DOI: https://doi.org/10.1007/978-3-662-04565-7_20
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