{"paper":{"title":"Faster Algorithms for All-Pairs Bounded Min-Cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amir Abboud, Daniel Wolleb-Graf, Giuseppe F. Italiano, Loukas Georgiadis, Nikos Parotsidis, Ohad Trabelsi, Przemys{\\l}aw Uzna\\'nski, Robert Krauthgamer","submitted_at":"2018-07-16T11:45:29Z","abstract_excerpt":"The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to edge/vertex connectivity). Our focus is on the $k$-bounded case, where the algorithm has to find all pairs with min-cut value less than $k$, and report only those. The most basic case $k=1$ is the Transitive Closure (TC) problem, which can be solved in graphs with $n$ vertices and $m$ edges in time $O(mn)$ combinatorially, and in time $O(n^{\\omega})$ where $\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05803","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}