{"paper":{"title":"The matching problem has no small symmetric SDP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Arefin Huq, Aurko Roy, Benjamin Weitz, Daniel Zink, G\\'abor Braun, Jonah Brown-Cohen, Prasad Raghavendra, Sebastian Pokutta","submitted_at":"2015-04-02T22:31:41Z","abstract_excerpt":"Yannakakis showed that the matching problem does not have a small symmetric linear program. Rothvo{\\ss} recently proved that any, not necessarily symmetric, linear program also has exponential size. It is natural to ask whether the matching problem can be expressed compactly in a framework such as semidefinite programming (SDP) that is more powerful than linear programming but still allows efficient optimization. We answer this question negatively for symmetric SDPs: any symmetric SDP for the matching problem has exponential size.\n  We also show that an O(k)-round Lasserre SDP relaxation for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00703","kind":"arxiv","version":5},"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"}