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October 2, 2025Open Access

Improved Directed Expander Decompositions

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New algorithms improve directed expander decomposition efficiency in capacitated graphs, suggesting broader applications.

The proposed algorithms achieve faster expander decomposition for directed graphs, addressing previous technical hurdles.
First directed expander decomposition algorithm for capacitated graphs runs in near-linear time with optimal dependence on phi.
Implementation and analysis of the non-stop cut-matching game advance understanding of directed, capacitated graphs.
This research highlights how methods from undirected graphs can be adapted to tackle directed graph challenges.

Fleischmann et al. (2025) studied this question.

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