{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HVCI5NDRWQAQ2RMKE7P6NZLBZW","short_pith_number":"pith:HVCI5NDR","schema_version":"1.0","canonical_sha256":"3d448eb471b4010d458a27dfe6e561cd92eee5a865ef37b84a000728dc655bf3","source":{"kind":"arxiv","id":"1806.07356","version":2},"attestation_state":"computed","paper":{"title":"Deterministic $O(1)$-Approximation Algorithms to 1-Center Clustering with Outliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Shyam Narayanan","submitted_at":"2018-06-19T17:39:46Z","abstract_excerpt":"The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant $0 < \\alpha < 1$ and $n$ points such that $\\alpha n$ of them are in some (unknown) ball of radius $r,$ the goal is to compute a ball of radius $O(r)$ that also contains $\\alpha n$ points. This problem can be formulated with the points in a normed vector space such as $\\mathbb{R}^d$ or in a general metric space.\n  The problem has a simple randomized solution: a randomly selected point is a correct solution with constant p"},"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":"1806.07356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-19T17:39:46Z","cross_cats_sorted":[],"title_canon_sha256":"e6d0301c60f1b32cdd7ea92e6c34f77f6333a2fa5ce57d1e212f035db2ef3d02","abstract_canon_sha256":"b00ef43f9b569513a0179509bcc7b8a696a322bcc930d1b481db8500692e3c9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:39.271853Z","signature_b64":"gvq8PqG3QPQ/XkEb6x76sSYLOODwvZO7ai1SALz2N8a1PjxhgZWuYipzl1b2TMXWxW0HvmbMQmnKH2m8njHHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d448eb471b4010d458a27dfe6e561cd92eee5a865ef37b84a000728dc655bf3","last_reissued_at":"2026-05-18T00:04:39.271447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:39.271447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deterministic $O(1)$-Approximation Algorithms to 1-Center Clustering with Outliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Shyam Narayanan","submitted_at":"2018-06-19T17:39:46Z","abstract_excerpt":"The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant $0 < \\alpha < 1$ and $n$ points such that $\\alpha n$ of them are in some (unknown) ball of radius $r,$ the goal is to compute a ball of radius $O(r)$ that also contains $\\alpha n$ points. This problem can be formulated with the points in a normed vector space such as $\\mathbb{R}^d$ or in a general metric space.\n  The problem has a simple randomized solution: a randomly selected point is a correct solution with constant p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07356","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":"1806.07356","created_at":"2026-05-18T00:04:39.271507+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.07356v2","created_at":"2026-05-18T00:04:39.271507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07356","created_at":"2026-05-18T00:04:39.271507+00:00"},{"alias_kind":"pith_short_12","alias_value":"HVCI5NDRWQAQ","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HVCI5NDRWQAQ2RMK","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HVCI5NDR","created_at":"2026-05-18T12:32:28.185984+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/HVCI5NDRWQAQ2RMKE7P6NZLBZW","json":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW.json","graph_json":"https://pith.science/api/pith-number/HVCI5NDRWQAQ2RMKE7P6NZLBZW/graph.json","events_json":"https://pith.science/api/pith-number/HVCI5NDRWQAQ2RMKE7P6NZLBZW/events.json","paper":"https://pith.science/paper/HVCI5NDR"},"agent_actions":{"view_html":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW","download_json":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW.json","view_paper":"https://pith.science/paper/HVCI5NDR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.07356&json=true","fetch_graph":"https://pith.science/api/pith-number/HVCI5NDRWQAQ2RMKE7P6NZLBZW/graph.json","fetch_events":"https://pith.science/api/pith-number/HVCI5NDRWQAQ2RMKE7P6NZLBZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW/action/storage_attestation","attest_author":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW/action/author_attestation","sign_citation":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW/action/citation_signature","submit_replication":"https://pith.science/pith/HVCI5NDRWQAQ2RMKE7P6NZLBZW/action/replication_record"}},"created_at":"2026-05-18T00:04:39.271507+00:00","updated_at":"2026-05-18T00:04:39.271507+00:00"}