Improved approximation for directed cut problems

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Amit Agarwal, Noga Alon, Moses Charikar

Published: 2007, Last Modified: 06 Nov 2025STOC 2007EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We present improved approximation algorithms for directed multicutand directed sparsest cut. The current best known approximationratio for these problems is O(n1/2). We obtain an Õ(n11/23)-approximation. Our algorithm works with thenatural LP relaxation used in prior work. We use a randomized roundingalgorithm with a more sophisticated charging scheme and analysis toobtain our improvement. This also implies a Õ(n11/23) upper bound on the ratio between the maximum multicommodity flowand minimum multicut in directed graphs.