2026-09-05T11:38:48Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26480 2026-08-27T14:40:29Z ddc:004 open_access

Faster Weak Expander Decompositions and Approximate Max Flow Fleischmann, Henry Li, George Z. Li, Jason max flow expander decompositions congestion approximators cut-matching game We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game when computing weak expander decompositions, avoiding the cost of the recursion depth. Our algorithm is also flexible enough to support weaker flow subroutines than previous algorithms. Our second contribution is to streamline the recent non-recursive approximate max flow algorithm of Li, Rao, and Wang (SODA, 2025) and adapt their framework to use our new weak expander decomposition primitive. Consequently, we give an approximate max flow algorithm within a few logarithmic factors of the limit of expander decomposition-based approaches. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Henry Fleischmann and George Z. Li and Jason Li 2026 Is Part Of LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2026.91 urn:nbn:de:0030-drops-264800 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.91 eng https://creativecommons.org/licenses/by/4.0/legalcode