{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:H3SHDKWN7HO4XYYY66ZOUVHFHN","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":"394454f5e4835c6a7a1d62113bd33b1c6e89173462a5ae0b7d335d2b3fac8afd","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-04T08:05:34Z","title_canon_sha256":"58a5c5f572aa74a151b1e8f33d22cd35c2fc472efffabd8b7d2d7a18f64ca63c"},"schema_version":"1.0","source":{"id":"2502.02085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.02085","created_at":"2026-07-05T10:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"2502.02085v1","created_at":"2026-07-05T10:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02085","created_at":"2026-07-05T10:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"H3SHDKWN7HO4","created_at":"2026-07-05T10:09:23Z"},{"alias_kind":"pith_short_16","alias_value":"H3SHDKWN7HO4XYYY","created_at":"2026-07-05T10:09:23Z"},{"alias_kind":"pith_short_8","alias_value":"H3SHDKWN","created_at":"2026-07-05T10:09:23Z"}],"graph_snapshots":[{"event_id":"sha256:5cfba28096b81a8c85ffeddfb0f7422e03ab19b0fd0e28518e0472443772bef0","target":"graph","created_at":"2026-07-05T10:09:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.02085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $k$-$\\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\\mathcal{X} \\subset \\mathbb{R} ^d$ into $k$ clusters.\n  The popularity of this algorithm is due to its simplicity and provable guarantee of being $O(\\log k)$ competitive with the optimal solution in expectation. However, its running time is $O(|\\mathcal{X}|kd)$, making it expensive for large datasets.\n  In this work, we present a simple and effective rejection sampling based approach for speeding up $k$-$\\mathtt{mean","authors_text":"Poojan Shah, Ragesh Jaiswal, Shashwat Agrawal","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-04T08:05:34Z","title":"A New Rejection Sampling Approach to $k$-$\\mathtt{means}$++ With Improved Trade-Offs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02085","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":"sha256:9aa69f27ba2a428b2ed91f10aed8cfa5b51c85e4bafd427085d438bf539f3ca9","target":"record","created_at":"2026-07-05T10:09:23Z","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":"394454f5e4835c6a7a1d62113bd33b1c6e89173462a5ae0b7d335d2b3fac8afd","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-04T08:05:34Z","title_canon_sha256":"58a5c5f572aa74a151b1e8f33d22cd35c2fc472efffabd8b7d2d7a18f64ca63c"},"schema_version":"1.0","source":{"id":"2502.02085","kind":"arxiv","version":1}},"canonical_sha256":"3ee471aacdf9ddcbe318f7b2ea54e53b7c60937e79a36f3c390eac9f70cfe10c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ee471aacdf9ddcbe318f7b2ea54e53b7c60937e79a36f3c390eac9f70cfe10c","first_computed_at":"2026-07-05T10:09:23.558964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:09:23.558964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9LCbViVumU3zLGaSk5hRs3s7yCYCgd2m/VyO1Fc0z1uxqbL+Cl+ZdYtSQ4O7iYXCWi/qLFm9D/r5Q+TVmp1PCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:09:23.559390Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.02085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9aa69f27ba2a428b2ed91f10aed8cfa5b51c85e4bafd427085d438bf539f3ca9","sha256:5cfba28096b81a8c85ffeddfb0f7422e03ab19b0fd0e28518e0472443772bef0"],"state_sha256":"740329fec665243a1533e1606099bbecede6f7ad452f591a6c0dcb2cd41db7cf"}