{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NXFMDTCX23MUDAMJCOCQ34UBAL","short_pith_number":"pith:NXFMDTCX","schema_version":"1.0","canonical_sha256":"6dcac1cc57d6d941818913850df28102daef033bdcc0369b7bb89c5367345ed2","source":{"kind":"arxiv","id":"1902.03519","version":2},"attestation_state":"computed","paper":{"title":"Scalable Fair Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Ali Vakilian, Arturs Backurs, Baruch Schieber, Krzysztof Onak, Piotr Indyk, Tal Wagner","submitted_at":"2019-02-10T00:04:34Z","abstract_excerpt":"We study the fair variant of the classic $k$-median problem introduced by Chierichetti et al. [2017]. In the standard $k$-median problem, given an input pointset $P$, the goal is to find $k$ centers $C$ and assign each input point to one of the centers in $C$ such that the average distance of points to their cluster center is minimized.\n  In the fair variant of $k$-median, the points are colored, and the goal is to minimize the same average distance objective while ensuring that all clusters have an \"approximately equal\" number of points of each color.\n  Chierichetti et al. proposed a two-phas"},"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":"1902.03519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-10T00:04:34Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"646c63c655f92ef85adc413d91f676e0f03ba3341cdc039c5ccb5a753b28ebe8","abstract_canon_sha256":"825ad73efc867d8d2459331112b0ce6ac76c9088bde0fc51dbbfa9b1972cf5aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:42.600422Z","signature_b64":"rObvUdSAt+1cK5rpmqyHK7Va3l8XhfGSElGzgix3eGPXBrMOmGHAc2teJzQUFC7yVG7n6t70Qd9yLIHOpq9gBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dcac1cc57d6d941818913850df28102daef033bdcc0369b7bb89c5367345ed2","last_reissued_at":"2026-05-17T23:43:42.599655Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:42.599655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalable Fair Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Ali Vakilian, Arturs Backurs, Baruch Schieber, Krzysztof Onak, Piotr Indyk, Tal Wagner","submitted_at":"2019-02-10T00:04:34Z","abstract_excerpt":"We study the fair variant of the classic $k$-median problem introduced by Chierichetti et al. [2017]. In the standard $k$-median problem, given an input pointset $P$, the goal is to find $k$ centers $C$ and assign each input point to one of the centers in $C$ such that the average distance of points to their cluster center is minimized.\n  In the fair variant of $k$-median, the points are colored, and the goal is to minimize the same average distance objective while ensuring that all clusters have an \"approximately equal\" number of points of each color.\n  Chierichetti et al. proposed a two-phas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03519","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":"1902.03519","created_at":"2026-05-17T23:43:42.599791+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03519v2","created_at":"2026-05-17T23:43:42.599791+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03519","created_at":"2026-05-17T23:43:42.599791+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXFMDTCX23MU","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXFMDTCX23MUDAMJ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXFMDTCX","created_at":"2026-05-18T12:33:24.271573+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/NXFMDTCX23MUDAMJCOCQ34UBAL","json":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL.json","graph_json":"https://pith.science/api/pith-number/NXFMDTCX23MUDAMJCOCQ34UBAL/graph.json","events_json":"https://pith.science/api/pith-number/NXFMDTCX23MUDAMJCOCQ34UBAL/events.json","paper":"https://pith.science/paper/NXFMDTCX"},"agent_actions":{"view_html":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL","download_json":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL.json","view_paper":"https://pith.science/paper/NXFMDTCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03519&json=true","fetch_graph":"https://pith.science/api/pith-number/NXFMDTCX23MUDAMJCOCQ34UBAL/graph.json","fetch_events":"https://pith.science/api/pith-number/NXFMDTCX23MUDAMJCOCQ34UBAL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL/action/storage_attestation","attest_author":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL/action/author_attestation","sign_citation":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL/action/citation_signature","submit_replication":"https://pith.science/pith/NXFMDTCX23MUDAMJCOCQ34UBAL/action/replication_record"}},"created_at":"2026-05-17T23:43:42.599791+00:00","updated_at":"2026-05-17T23:43:42.599791+00:00"}