{"paper":{"title":"Computing minimum cuts in hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chandra Chekuri, Chao Xu","submitted_at":"2016-07-29T03:22:56Z","abstract_excerpt":"We study algorithmic and structural aspects of connectivity in hypergraphs. Given a hypergraph $H=(V,E)$ with $n = |V|$, $m = |E|$ and $p = \\sum_{e \\in E} |e|$ the best known algorithm to compute a global minimum cut in $H$ runs in time $O(np)$ for the uncapacitated case and in $O(np + n^2 \\log n)$ time for the capacitated case. We show the following new results.\n  1. Given an uncapacitated hypergraph $H$ and an integer $k$ we describe an algorithm that runs in $O(p)$ time to find a subhypergraph $H'$ with sum of degrees $O(kn)$ that preserves all edge-connectivities up to $k$ (a $k$-sparsifie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08682","kind":"arxiv","version":3},"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"}