{"paper":{"title":"Cheeger-type approximation for sparsest $st$-cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Robert Krauthgamer, Tal Wagner","submitted_at":"2014-10-14T23:05:57Z","abstract_excerpt":"We introduce the $st$-cut version the Sparsest-Cut problem, where the goal is to find a cut of minimum sparsity among those separating two distinguished vertices $s,t\\in V$. Clearly, this problem is at least as hard as the usual (non-$st$) version. Our main result is a polynomial-time algorithm for the product-demands setting, that produces a cut of sparsity $O(\\sqrt{\\OPT})$, where $\\OPT$ denotes the optimum, and the total edge capacity and the total demand are assumed (by normalization) to be $1$.\n  Our result generalizes the recent work of Trevisan [arXiv, 2013] for the non-$st$ version of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3889","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"}