{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ZNLZAKEY7Y2J5DN6QJY22DMI2M","short_pith_number":"pith:ZNLZAKEY","schema_version":"1.0","canonical_sha256":"cb57902898fe349e8dbe8271ad0d88d3367b7c627715a07113d40cb170867a36","source":{"kind":"arxiv","id":"2211.06033","version":1},"attestation_state":"computed","paper":{"title":"A Faster Small Treewidth SDP Solver","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.OC","authors_text":"Yuzhou Gu, Zhao Song","submitted_at":"2022-11-11T07:09:31Z","abstract_excerpt":"Semidefinite programming is a fundamental tool in optimization and theoretical computer science. It has been extensively used as a black-box for solving many problems, such as embedding, complexity, learning, and discrepancy.\n  One natural setting of semidefinite programming is the small treewidth setting. The best previous SDP solver under small treewidth setting is due to Zhang-Lavaei '18, which takes $n^{1.5} \\tau^{6.5}$ time. In this work, we show how to solve a semidefinite programming with $n \\times n$ variables, $m$ constraints and $\\tau$ treewidth in $n \\tau^{2\\omega+0.5}$ time, where "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.06033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-11T07:09:31Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e1ccdf9e5746aba4a89eb3a408950df10dde458b05fd5003f3a01a9c4e996a46","abstract_canon_sha256":"86a74b9373b2ffc8fa41fe5e774601408b1e177b650555e6473f5c8ed71fdd90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:15:16.420265Z","signature_b64":"sCVucuJaeWxR8u/8Vy1IuRRa6nAaJPK67nts4XJECXov/AB/ROmIdFUobtt4jJoFsYMGXZJCbXCKSjVY6w+ZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb57902898fe349e8dbe8271ad0d88d3367b7c627715a07113d40cb170867a36","last_reissued_at":"2026-07-05T05:15:16.419854Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:15:16.419854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Faster Small Treewidth SDP Solver","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.OC","authors_text":"Yuzhou Gu, Zhao Song","submitted_at":"2022-11-11T07:09:31Z","abstract_excerpt":"Semidefinite programming is a fundamental tool in optimization and theoretical computer science. It has been extensively used as a black-box for solving many problems, such as embedding, complexity, learning, and discrepancy.\n  One natural setting of semidefinite programming is the small treewidth setting. The best previous SDP solver under small treewidth setting is due to Zhang-Lavaei '18, which takes $n^{1.5} \\tau^{6.5}$ time. In this work, we show how to solve a semidefinite programming with $n \\times n$ variables, $m$ constraints and $\\tau$ treewidth in $n \\tau^{2\\omega+0.5}$ time, where "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.06033","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.06033/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.06033","created_at":"2026-07-05T05:15:16.419911+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.06033v1","created_at":"2026-07-05T05:15:16.419911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.06033","created_at":"2026-07-05T05:15:16.419911+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZNLZAKEY7Y2J","created_at":"2026-07-05T05:15:16.419911+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZNLZAKEY7Y2J5DN6","created_at":"2026-07-05T05:15:16.419911+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZNLZAKEY","created_at":"2026-07-05T05:15:16.419911+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2306.14048","citing_title":"H$_2$O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models","ref_index":140,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M","json":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M.json","graph_json":"https://pith.science/api/pith-number/ZNLZAKEY7Y2J5DN6QJY22DMI2M/graph.json","events_json":"https://pith.science/api/pith-number/ZNLZAKEY7Y2J5DN6QJY22DMI2M/events.json","paper":"https://pith.science/paper/ZNLZAKEY"},"agent_actions":{"view_html":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M","download_json":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M.json","view_paper":"https://pith.science/paper/ZNLZAKEY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.06033&json=true","fetch_graph":"https://pith.science/api/pith-number/ZNLZAKEY7Y2J5DN6QJY22DMI2M/graph.json","fetch_events":"https://pith.science/api/pith-number/ZNLZAKEY7Y2J5DN6QJY22DMI2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M/action/storage_attestation","attest_author":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M/action/author_attestation","sign_citation":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M/action/citation_signature","submit_replication":"https://pith.science/pith/ZNLZAKEY7Y2J5DN6QJY22DMI2M/action/replication_record"}},"created_at":"2026-07-05T05:15:16.419911+00:00","updated_at":"2026-07-05T05:15:16.419911+00:00"}