{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TKFLNHHR26SPNDMRJR57IVKVRQ","short_pith_number":"pith:TKFLNHHR","schema_version":"1.0","canonical_sha256":"9a8ab69cf1d7a4f68d914c7bf455558c30abe9532cb96ed473daf6b43ed6062c","source":{"kind":"arxiv","id":"1904.12334","version":1},"attestation_state":"computed","paper":{"title":"Tight FPT Approximations for $k$-Median and $k$-Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amit Kumar, Anupam Gupta, Euiwoong Lee, Jason Li, Vincent Cohen-Addad","submitted_at":"2019-04-28T15:10:07Z","abstract_excerpt":"We investigate the fine-grained complexity of approximating the classical $k$-median / $k$-means clustering problems in general metric spaces. We show how to improve the approximation factors to $(1+2/e+\\varepsilon)$ and $(1+8/e+\\varepsilon)$ respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures."},"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":"1904.12334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-28T15:10:07Z","cross_cats_sorted":[],"title_canon_sha256":"983e73e7182867de7fa6c4d5af26c68372dbb012a64c8f00243f502c2b75c959","abstract_canon_sha256":"aa9940cbb0ba3581881c576a1c647a02e070529c7e0cb3022c7d8b0d0a27d01b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:36.751799Z","signature_b64":"DMURzmgX51n3zDSxf0lJmT3cL5BWf3eiHe1fSh9A4jOJmujeCsLU8vkedhIhWfXCfMUE3U+BJ6Xt0w6cYeYDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a8ab69cf1d7a4f68d914c7bf455558c30abe9532cb96ed473daf6b43ed6062c","last_reissued_at":"2026-05-17T23:47:36.751146Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:36.751146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight FPT Approximations for $k$-Median and $k$-Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amit Kumar, Anupam Gupta, Euiwoong Lee, Jason Li, Vincent Cohen-Addad","submitted_at":"2019-04-28T15:10:07Z","abstract_excerpt":"We investigate the fine-grained complexity of approximating the classical $k$-median / $k$-means clustering problems in general metric spaces. We show how to improve the approximation factors to $(1+2/e+\\varepsilon)$ and $(1+8/e+\\varepsilon)$ respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12334","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":"1904.12334","created_at":"2026-05-17T23:47:36.751249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.12334v1","created_at":"2026-05-17T23:47:36.751249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12334","created_at":"2026-05-17T23:47:36.751249+00:00"},{"alias_kind":"pith_short_12","alias_value":"TKFLNHHR26SP","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"TKFLNHHR26SPNDMR","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"TKFLNHHR","created_at":"2026-05-18T12:33:30.264802+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/TKFLNHHR26SPNDMRJR57IVKVRQ","json":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ.json","graph_json":"https://pith.science/api/pith-number/TKFLNHHR26SPNDMRJR57IVKVRQ/graph.json","events_json":"https://pith.science/api/pith-number/TKFLNHHR26SPNDMRJR57IVKVRQ/events.json","paper":"https://pith.science/paper/TKFLNHHR"},"agent_actions":{"view_html":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ","download_json":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ.json","view_paper":"https://pith.science/paper/TKFLNHHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.12334&json=true","fetch_graph":"https://pith.science/api/pith-number/TKFLNHHR26SPNDMRJR57IVKVRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/TKFLNHHR26SPNDMRJR57IVKVRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ/action/storage_attestation","attest_author":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ/action/author_attestation","sign_citation":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ/action/citation_signature","submit_replication":"https://pith.science/pith/TKFLNHHR26SPNDMRJR57IVKVRQ/action/replication_record"}},"created_at":"2026-05-17T23:47:36.751249+00:00","updated_at":"2026-05-17T23:47:36.751249+00:00"}