{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TKFLNHHR26SPNDMRJR57IVKVRQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aa9940cbb0ba3581881c576a1c647a02e070529c7e0cb3022c7d8b0d0a27d01b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-28T15:10:07Z","title_canon_sha256":"983e73e7182867de7fa6c4d5af26c68372dbb012a64c8f00243f502c2b75c959"},"schema_version":"1.0","source":{"id":"1904.12334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12334","created_at":"2026-05-17T23:47:36Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12334v1","created_at":"2026-05-17T23:47:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12334","created_at":"2026-05-17T23:47:36Z"},{"alias_kind":"pith_short_12","alias_value":"TKFLNHHR26SP","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TKFLNHHR26SPNDMR","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TKFLNHHR","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:c26afeb17767fdc4860500d220bb8f6bcae7910b33a2474247198ee8bcb7b3b9","target":"graph","created_at":"2026-05-17T23:47:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Amit Kumar, Anupam Gupta, Euiwoong Lee, Jason Li, Vincent Cohen-Addad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-28T15:10:07Z","title":"Tight FPT Approximations for $k$-Median and $k$-Means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12334","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:42b26af4c55f4587c71d7eb83d8ddc996ee6ed76277299a5ef86a078906e20dc","target":"record","created_at":"2026-05-17T23:47:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aa9940cbb0ba3581881c576a1c647a02e070529c7e0cb3022c7d8b0d0a27d01b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-28T15:10:07Z","title_canon_sha256":"983e73e7182867de7fa6c4d5af26c68372dbb012a64c8f00243f502c2b75c959"},"schema_version":"1.0","source":{"id":"1904.12334","kind":"arxiv","version":1}},"canonical_sha256":"9a8ab69cf1d7a4f68d914c7bf455558c30abe9532cb96ed473daf6b43ed6062c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a8ab69cf1d7a4f68d914c7bf455558c30abe9532cb96ed473daf6b43ed6062c","first_computed_at":"2026-05-17T23:47:36.751146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:36.751146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMURzmgX51n3zDSxf0lJmT3cL5BWf3eiHe1fSh9A4jOJmujeCsLU8vkedhIhWfXCfMUE3U+BJ6Xt0w6cYeYDCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:36.751799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42b26af4c55f4587c71d7eb83d8ddc996ee6ed76277299a5ef86a078906e20dc","sha256:c26afeb17767fdc4860500d220bb8f6bcae7910b33a2474247198ee8bcb7b3b9"],"state_sha256":"92d2b8c752a9b300fa698f032a6a39215a85c4e92e651a0e48bc8c16a46e88f0"}