Approximating Directed Multicuts

Authors:
Joseph Cheriyan;Howard Karloff;Yuval Rabani†
Affiliations:
Department of Combinatorics and Optimization Waterloo, University of Waterloo, Ontario, N2L 3G1, Canada;AT&T Labs––Research, 180 Park Ave., Florham Park, NJ 07932, USA;Computer Science Department Technion—IIT, 180 Park Ave., Haifa 32000, Israel
Venue:
Combinatorica
Year:
2005

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Abstract

The seminal paper of Leighton and 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. This 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 max flow-to-min multicut ratio. Our results are algorithmic, demonstrating nontrivial approximation guarantees.