{"paper":{"title":"The Complexity of Approximating Vertex Expansion","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anand Louis, Prasad Raghavendra, Santosh Vempala","submitted_at":"2013-04-10T20:31:28Z","abstract_excerpt":"We study the complexity of approximating the vertex expansion of graphs $G = (V,E)$, defined as \\[ \\Phi^V := \\min_{S \\subset V} n \\cdot \\frac{|N(S)|}{|S| |V \\backslash S|}. \\]\n  We give a simple polynomial-time algorithm for finding a subset with vertex expansion $O(\\sqrt{OPT \\log d})$ where $d$ is the maximum degree of the graph. Our main result is an asymptotically matching lower bound: under the Small Set Expansion (SSE) hypothesis, it is hard to find a subset with expansion less than $C\\sqrt{OPT \\log d}$ for an absolute constant $C$. In particular, this implies for all constant $\\epsilon >"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3139","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"}