{"paper":{"title":"Approximation Algorithms for Finding Maximum Induced Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alireza Rezaei, Shayan Oveis Gharan","submitted_at":"2015-11-09T17:56:29Z","abstract_excerpt":"We initiate the study of approximating the largest induced expander in a given graph $G$. Given a $\\Delta$-regular graph $G$ with $n$ vertices, the goal is to find the set with the largest induced expansion of size at least $\\delta \\cdot n$. We design a bi-criteria approximation algorithm for this problem; if the optimum has induced spectral expansion $\\lambda$ our algorithm returns a $\\frac{\\lambda}{\\log^2\\delta \\exp(\\Delta/\\lambda)}$-(spectral) expander of size at least $\\delta n$ (up to constants).\n  Our proof introduces and employs a novel semidefinite programming relaxation for the larges"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02786","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"}