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Approximating directed multicuts

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3 Author(s)
Cheriyan, J. ; Dept. of Combinatorics & Optimization, Waterloo Univ., Ont., Canada ; Karloff, H. ; Rabani, Y.

The seminal paper of F.T. Leighton and S. Rao (1988) and subsequent papers presented approximate min-max theorems relating multicommodity flow values and cut capacities in undirected networks, developed the divide-and-conquer method for designing approximation algorithms, and generated novel tools for utilizing linear programming relaxations. Yet, despite persistent research efforts, these achievements could not be extended to directed networks, excluding a few cases that are "symmetric" and therefore similar to undirected networks. The paper is an attempt to remedy the situation. We consider the problem of finding a minimum multicut in a directed multicommodity flow network, and give the first nontrivial upper bounds on the maxflow-to-min multicut ratio. Our results are algorithmic, demonstrating nontrivial approximation guarantees.

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001