We present improved approximation algorithms for directed multicut and directed sparsest cut. The current best known approximation ratio for these problems is O(n 1/2 ). We obtain anÕ(n 11/23 )-approximation. Our algorithm works with the natural LP relaxation used in prior work. We use a randomized rounding algorithm with a more sophisticated charging scheme and analysis to obtain our improvement. This also implies aÕ(n 11/23 ) upper bound on the ratio between the maximum multicommodity flow and minimum multicut in directed graphs.
al. REF to añ O(n 11/23 ) ratio approximation.
Improved approximation for directed cut problems
STOC '07
Mathematics Computer Science