{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AJ6SMGUXSLRR7GEXFYLMJGTWBF","short_pith_number":"pith:AJ6SMGUX","schema_version":"1.0","canonical_sha256":"027d261a9792e31f98972e16c49a76097be1f18648b7caf47fe91ee2223d33d9","source":{"kind":"arxiv","id":"1401.5170","version":2},"attestation_state":"computed","paper":{"title":"Eigenvalue, Quadratic Programming, and Semidefinite Programming Bounds for a Cut Minimization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hao Sun, Henry Wolkowicz, Ningchuan Wang, Ting Kei Pong","submitted_at":"2014-01-21T04:04:01Z","abstract_excerpt":"We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \\emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex separator. This problem is closely related to the graph partitioning problem. In fact, the model we use is the same as that for the graph partitioning problem except for a different \\emph{quadratic} objective function. We look at known and new bounds obtained from various relaxations for this NP-hard problem. This includes: the standard eigenvalue bound, proje"},"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":"1401.5170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-21T04:04:01Z","cross_cats_sorted":[],"title_canon_sha256":"a307b6fa3535c63308d818dc623307f7095646958ac9db72dbcab571d3c1288c","abstract_canon_sha256":"b5827ce260ae57fba33b0a6e481c165bc0259de96b0fd6d4aceb4a649cad28d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:45.011155Z","signature_b64":"2GqsgOeU0R4TNKOWz+uIYLdGrsKnBkKWdFRtmwWqE3ciQTBU1eIA4pRwcZs8pjeUDHHfEAVJHA/ppNThTZDrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"027d261a9792e31f98972e16c49a76097be1f18648b7caf47fe91ee2223d33d9","last_reissued_at":"2026-05-18T02:34:45.010790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:45.010790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalue, Quadratic Programming, and Semidefinite Programming Bounds for a Cut Minimization Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hao Sun, Henry Wolkowicz, Ningchuan Wang, Ting Kei Pong","submitted_at":"2014-01-21T04:04:01Z","abstract_excerpt":"We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \\emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex separator. This problem is closely related to the graph partitioning problem. In fact, the model we use is the same as that for the graph partitioning problem except for a different \\emph{quadratic} objective function. We look at known and new bounds obtained from various relaxations for this NP-hard problem. This includes: the standard eigenvalue bound, proje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5170","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":""},"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":"1401.5170","created_at":"2026-05-18T02:34:45.010845+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.5170v2","created_at":"2026-05-18T02:34:45.010845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5170","created_at":"2026-05-18T02:34:45.010845+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJ6SMGUXSLRR","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJ6SMGUXSLRR7GEX","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJ6SMGUX","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF","json":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF.json","graph_json":"https://pith.science/api/pith-number/AJ6SMGUXSLRR7GEXFYLMJGTWBF/graph.json","events_json":"https://pith.science/api/pith-number/AJ6SMGUXSLRR7GEXFYLMJGTWBF/events.json","paper":"https://pith.science/paper/AJ6SMGUX"},"agent_actions":{"view_html":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF","download_json":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF.json","view_paper":"https://pith.science/paper/AJ6SMGUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.5170&json=true","fetch_graph":"https://pith.science/api/pith-number/AJ6SMGUXSLRR7GEXFYLMJGTWBF/graph.json","fetch_events":"https://pith.science/api/pith-number/AJ6SMGUXSLRR7GEXFYLMJGTWBF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF/action/storage_attestation","attest_author":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF/action/author_attestation","sign_citation":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF/action/citation_signature","submit_replication":"https://pith.science/pith/AJ6SMGUXSLRR7GEXFYLMJGTWBF/action/replication_record"}},"created_at":"2026-05-18T02:34:45.010845+00:00","updated_at":"2026-05-18T02:34:45.010845+00:00"}