{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:M2Y2CJZBSGSGZOPNBAN2NCE64V","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":"7bb4d3c8259e9d130bd95b5a75ef4b74bcaa5f4fe5667438c8fe8658ed801480","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-07-02T02:07:12Z","title_canon_sha256":"ae9f4c7c9cdd4bfb1ae9483533188020574aca9c7d25f7c24cf2288b438ca5de"},"schema_version":"1.0","source":{"id":"2107.00798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.00798","created_at":"2026-07-05T03:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"2107.00798v2","created_at":"2026-07-05T03:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.00798","created_at":"2026-07-05T03:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"M2Y2CJZBSGSG","created_at":"2026-07-05T03:02:56Z"},{"alias_kind":"pith_short_16","alias_value":"M2Y2CJZBSGSGZOPN","created_at":"2026-07-05T03:02:56Z"},{"alias_kind":"pith_short_8","alias_value":"M2Y2CJZB","created_at":"2026-07-05T03:02:56Z"}],"graph_snapshots":[{"event_id":"sha256:d4e6b5b297fcf7183531bf8d280579c60589f3fda91d8da87cc18c5a5f85d4f9","target":"graph","created_at":"2026-07-05T03:02:56Z","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/2107.00798/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of explainable $k$-medians and $k$-means introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian~(ICML 2020). In this problem, our goal is to find a threshold decision tree that partitions data into $k$ clusters and minimizes the $k$-medians or $k$-means objective. The obtained clustering is easy to interpret because every decision node of a threshold tree splits data based on a single feature into two groups. We propose a new algorithm for this problem which is $\\tilde O(\\log k)$ competitive with $k$-medians with $\\ell_1$ norm and $\\tilde O(k)$ competitive with $k$-m","authors_text":"Konstantin Makarychev, Liren Shan","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-07-02T02:07:12Z","title":"Near-optimal Algorithms for Explainable k-Medians and k-Means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.00798","kind":"arxiv","version":2},"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":"sha256:293e724754d02ffaf2fa7dd7a8c22c09f28f68b5e371443e3aec9e836a43a133","target":"record","created_at":"2026-07-05T03:02:56Z","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":"7bb4d3c8259e9d130bd95b5a75ef4b74bcaa5f4fe5667438c8fe8658ed801480","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-07-02T02:07:12Z","title_canon_sha256":"ae9f4c7c9cdd4bfb1ae9483533188020574aca9c7d25f7c24cf2288b438ca5de"},"schema_version":"1.0","source":{"id":"2107.00798","kind":"arxiv","version":2}},"canonical_sha256":"66b1a1272191a46cb9ed081ba6889ee5732ecb4579bd47d5cf63b72e1d8f516e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66b1a1272191a46cb9ed081ba6889ee5732ecb4579bd47d5cf63b72e1d8f516e","first_computed_at":"2026-07-05T03:02:56.511286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:02:56.511286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6deokPeOkiAMdJyHOAZqceQy5Vm9aKgR3GVqJn3Pw6Ne3eV52BClD6zvdKzyAPYaBTw1z/jnfjkMKFtLWSR/CA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:02:56.511686Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.00798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:293e724754d02ffaf2fa7dd7a8c22c09f28f68b5e371443e3aec9e836a43a133","sha256:d4e6b5b297fcf7183531bf8d280579c60589f3fda91d8da87cc18c5a5f85d4f9"],"state_sha256":"d2fb93d1af78a439899b4e0e05c59ab06a901dd636af3817cff1f4929f9a5c04"}