{"paper":{"title":"A $(\\log n)^{\\Omega(1)}$ integrality gap for the Sparsest Cut SDP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"cs.DS","authors_text":"Assaf Naor, Bruce Kleiner, Jeff Cheeger","submitted_at":"2009-10-11T17:39:05Z","abstract_excerpt":"We show that the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem with general demands has integrality gap $(\\log n)^{\\Omega(1)}$. This is achieved by exhibiting $n$-point metric spaces of negative type whose $L_1$ distortion is $(\\log n)^{\\Omega(1)}$. Our result is based on quantitative bounds on the rate of degeneration of Lipschitz maps from the Heisenberg group to $L_1$ when restricted to cosets of the center."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2024","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0910.2024/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}