{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GIFIDKULUG3DAAWFPH4D642GSM","short_pith_number":"pith:GIFIDKUL","schema_version":"1.0","canonical_sha256":"320a81aa8ba1b63002c579f83f7346931c42cd2ac3cb96c6d7ed4f7fc5dcd39c","source":{"kind":"arxiv","id":"1206.3603","version":1},"attestation_state":"computed","paper":{"title":"Approximation Algorithm for Non-Boolean MAX k-CSP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Konstantin Makarychev, Yury Makarychev","submitted_at":"2012-06-15T22:40:40Z","abstract_excerpt":"In this paper, we present a randomized polynomial-time approximation algorithm for k-CSPd. In k-CSPd, we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of satisfied constraints.\n  Our algorithm has approximation factor Omega(kd/d^k) (when k > \\Omega(log d)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Omega(k log d/d^k).\n  We also give an approximation algorithm for the boolean MAX k-CSP2 problem with a slightly improved a"},"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":"1206.3603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-06-15T22:40:40Z","cross_cats_sorted":[],"title_canon_sha256":"64eb417ff4b57c4b9033753eb6b29d52a91e3f3f9d08388d292c1d8588cbec70","abstract_canon_sha256":"de87cdabbcd88e2b5d0380fac6309c4a63fe4308b8c4578c9ae0e8bd63a891b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:19.358604Z","signature_b64":"43lMVFHzalvVFH8G8ulCSkz4ZVRTTQP7evt4zxRHs3nrwP8AppyeuiOiEfWnd8QUp2XzZBgFB8FfWalku6o2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"320a81aa8ba1b63002c579f83f7346931c42cd2ac3cb96c6d7ed4f7fc5dcd39c","last_reissued_at":"2026-05-18T03:53:19.357911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:19.357911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation Algorithm for Non-Boolean MAX k-CSP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Konstantin Makarychev, Yury Makarychev","submitted_at":"2012-06-15T22:40:40Z","abstract_excerpt":"In this paper, we present a randomized polynomial-time approximation algorithm for k-CSPd. In k-CSPd, we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of satisfied constraints.\n  Our algorithm has approximation factor Omega(kd/d^k) (when k > \\Omega(log d)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Omega(k log d/d^k).\n  We also give an approximation algorithm for the boolean MAX k-CSP2 problem with a slightly improved a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3603","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":""},"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":"1206.3603","created_at":"2026-05-18T03:53:19.358015+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3603v1","created_at":"2026-05-18T03:53:19.358015+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3603","created_at":"2026-05-18T03:53:19.358015+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIFIDKULUG3D","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIFIDKULUG3DAAWF","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIFIDKUL","created_at":"2026-05-18T12:27:06.952714+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/GIFIDKULUG3DAAWFPH4D642GSM","json":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM.json","graph_json":"https://pith.science/api/pith-number/GIFIDKULUG3DAAWFPH4D642GSM/graph.json","events_json":"https://pith.science/api/pith-number/GIFIDKULUG3DAAWFPH4D642GSM/events.json","paper":"https://pith.science/paper/GIFIDKUL"},"agent_actions":{"view_html":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM","download_json":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM.json","view_paper":"https://pith.science/paper/GIFIDKUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3603&json=true","fetch_graph":"https://pith.science/api/pith-number/GIFIDKULUG3DAAWFPH4D642GSM/graph.json","fetch_events":"https://pith.science/api/pith-number/GIFIDKULUG3DAAWFPH4D642GSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM/action/storage_attestation","attest_author":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM/action/author_attestation","sign_citation":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM/action/citation_signature","submit_replication":"https://pith.science/pith/GIFIDKULUG3DAAWFPH4D642GSM/action/replication_record"}},"created_at":"2026-05-18T03:53:19.358015+00:00","updated_at":"2026-05-18T03:53:19.358015+00:00"}