{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:M32ZY2NULRCNZMCPNFGYTRLMHD","short_pith_number":"pith:M32ZY2NU","schema_version":"1.0","canonical_sha256":"66f59c69b45c44dcb04f694d89c56c38f663d8823cad4995a979a00d44b6405b","source":{"kind":"arxiv","id":"2403.02971","version":3},"attestation_state":"computed","paper":{"title":"Space Complexity of Euclidean Clustering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Lingxiao Huang, Xiaoyi Zhu, Yuxiang Tian, Zengfeng Huang","submitted_at":"2024-03-05T13:49:32Z","abstract_excerpt":"The $(k, z)$-Clustering problem in Euclidean space $\\mathbb{R}^d$ has been extensively studied. Given the scale of data involved, compression methods for the Euclidean $(k, z)$-Clustering problem, such as data compression and dimension reduction, have received significant attention in the literature. However, the space complexity of the clustering problem, specifically, the number of bits required to compress the cost function within a multiplicative error $\\varepsilon$, remains unclear in existing literature. This paper initiates the study of space complexity for Euclidean $(k, z)$-Clustering"},"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":"2403.02971","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2024-03-05T13:49:32Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"27f01b88b4460c4599b4376ac69561948684b6764218f245db2a4fab93d187ae","abstract_canon_sha256":"4324b405f9a910b610c070ccd8ac3cd54a25b9709f4d65eff7238a84fe6c52fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:31:41.845205Z","signature_b64":"paptnlaEsSAh5Pk98LAvvWQUe2wK1jjs4CrT9DZ6O1LvmXzc3HqYGJq7QUPE32EpMCNuq/n6fF0PKyT8o9PpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66f59c69b45c44dcb04f694d89c56c38f663d8823cad4995a979a00d44b6405b","last_reissued_at":"2026-07-05T10:31:41.844660Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:31:41.844660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Space Complexity of Euclidean Clustering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Lingxiao Huang, Xiaoyi Zhu, Yuxiang Tian, Zengfeng Huang","submitted_at":"2024-03-05T13:49:32Z","abstract_excerpt":"The $(k, z)$-Clustering problem in Euclidean space $\\mathbb{R}^d$ has been extensively studied. Given the scale of data involved, compression methods for the Euclidean $(k, z)$-Clustering problem, such as data compression and dimension reduction, have received significant attention in the literature. However, the space complexity of the clustering problem, specifically, the number of bits required to compress the cost function within a multiplicative error $\\varepsilon$, remains unclear in existing literature. This paper initiates the study of space complexity for Euclidean $(k, z)$-Clustering"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.02971","kind":"arxiv","version":3},"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/2403.02971/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":"2403.02971","created_at":"2026-07-05T10:31:41.844723+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.02971v3","created_at":"2026-07-05T10:31:41.844723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.02971","created_at":"2026-07-05T10:31:41.844723+00:00"},{"alias_kind":"pith_short_12","alias_value":"M32ZY2NULRCN","created_at":"2026-07-05T10:31:41.844723+00:00"},{"alias_kind":"pith_short_16","alias_value":"M32ZY2NULRCNZMCP","created_at":"2026-07-05T10:31:41.844723+00:00"},{"alias_kind":"pith_short_8","alias_value":"M32ZY2NU","created_at":"2026-07-05T10:31:41.844723+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.16229","citing_title":"Fast, Space-Optimal Streaming Algorithms for Clustering and Subspace Embeddings","ref_index":54,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD","json":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD.json","graph_json":"https://pith.science/api/pith-number/M32ZY2NULRCNZMCPNFGYTRLMHD/graph.json","events_json":"https://pith.science/api/pith-number/M32ZY2NULRCNZMCPNFGYTRLMHD/events.json","paper":"https://pith.science/paper/M32ZY2NU"},"agent_actions":{"view_html":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD","download_json":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD.json","view_paper":"https://pith.science/paper/M32ZY2NU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.02971&json=true","fetch_graph":"https://pith.science/api/pith-number/M32ZY2NULRCNZMCPNFGYTRLMHD/graph.json","fetch_events":"https://pith.science/api/pith-number/M32ZY2NULRCNZMCPNFGYTRLMHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD/action/storage_attestation","attest_author":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD/action/author_attestation","sign_citation":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD/action/citation_signature","submit_replication":"https://pith.science/pith/M32ZY2NULRCNZMCPNFGYTRLMHD/action/replication_record"}},"created_at":"2026-07-05T10:31:41.844723+00:00","updated_at":"2026-07-05T10:31:41.844723+00:00"}