{"paper":{"title":"The Sketching Complexity of Graph Cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexandr Andoni, David P. Woodruff, Robert Krauthgamer","submitted_at":"2014-03-27T14:42:11Z","abstract_excerpt":"We study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on the dependence on the accuracy parameter $\\epsilon>0$.\n  First, we prove that for every $\\epsilon > 1/\\sqrt n$, every sketch that succeeds (with constant probability) in estimating the weight of all cuts $(S,\\bar S)$ in an $n$-vertex graph (simultaneously), must be of size $\\Omega(n/\\epsilon^2)$ bits. In the special case where the sketch is itself a weighted g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7058","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"}