{"paper":{"title":"Gap Amplification for Small-Set Expansion via Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Prasad Raghavendra, Tselil Schramm","submitted_at":"2013-10-05T16:35:35Z","abstract_excerpt":"In this work, we achieve gap amplification for the Small-Set Expansion problem. Specifically, we show that an instance of the Small-Set Expansion Problem with completeness $\\epsilon$ and soundness $\\frac{1}{2}$ is at least as difficult as Small-Set Expansion with completeness $\\epsilon$ and soundness $f(\\epsilon)$, for any function $f(\\epsilon)$ which grows faster than $\\sqrt{\\epsilon}$. We achieve this amplification via random walks -- our gadget is the graph with adjacency matrix corresponding to a random walk on the original graph. An interesting feature of our reduction is that unlike gap "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1493","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"}