{"paper":{"title":"Nearly optimal edge estimation with independent set queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amit Levi, Erik Waingarten, Xi Chen","submitted_at":"2019-07-09T19:48:24Z","abstract_excerpt":"We study the problem of estimating the number of edges of an unknown, undirected graph $G=([n],E)$ with access to an independent set oracle. When queried about a subset $S\\subseteq [n]$ of vertices the independent set oracle answers whether $S$ is an independent set in $G$ or not. Our first main result is an algorithm that computes a $(1+\\epsilon)$-approximation of the number of edges $m$ of the graph using $\\min(\\sqrt{m},n / \\sqrt{m})\\cdot\\textrm{poly}(\\log n,1/\\epsilon)$ independent set queries. This improves the upper bound of $\\min(\\sqrt{m},n^2/m)\\cdot\\textrm{poly}(\\log n,1/\\epsilon)$ by B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04381","kind":"arxiv","version":1},"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"}