TL;DR
This paper presents an efficient approximation algorithm for finding the sparsest cut in directed graphs, utilizing a cut-matching framework and only a logarithmic number of max-flow computations, thus improving computational efficiency.
Contribution
It introduces a novel O(log^2 n)-approximation algorithm for directed graph sparsest cut that reduces the number of max-flow computations needed.
Findings
Breaks the multicommodity-flow barrier for directed graphs
Uses only O(log^2 n) max-flow computations
Provides a provable approximation guarantee
Abstract
We give O(log^2 n)-approximation algorithm based on the cut-matching framework of [10, 13, 14] for computing the sparsest cut on directed graphs. Our algorithm uses only O(log^2 n) single commodity max-flow computations and thus breaks the multicommodity-flow barrier for computing the sparsest cut on directed graphs
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