{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D2ZLUXXDKGNVN2YVFWSPB2A5A3","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":"30cbd11021b497578ebf49fb941b1e138b36041dbaff243b2e00a82763f9f7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-27T06:29:35Z","title_canon_sha256":"a136ee2ef325a1f6ffda06baf08f920520dbeb16fc678033aecf49d914a1a884"},"schema_version":"1.0","source":{"id":"1009.5168","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5168","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5168v2","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5168","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"D2ZLUXXDKGNV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D2ZLUXXDKGNVN2YV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D2ZLUXXD","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:17f32b832738522e88652dc61adab78dbc18a653929255e9b014be67d4ae6387","target":"graph","created_at":"2026-05-18T04:22:40Z","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"},"paper":{"abstract_excerpt":"Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that given a point s in S return the distances between s and all other points. We show that given a natural assumption about the structure of the instance, we can efficiently find an accurate clustering using only O(k) distance queries. Our algorithm uses an active selection strategy to choose a small set of points that we call landmarks, and considers only the d","authors_text":"Heiko Roglin, Konstantin Voevodski, Maria-Florina Balcan, Shang-Hua Teng, Yu Xia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-27T06:29:35Z","title":"Efficient Clustering with Limited Distance Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5168","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:f702dbfb29292b719356c58cf2a3c27d9ab5c6f6e5d5a4f87d918a9dc3691ef0","target":"record","created_at":"2026-05-18T04:22:40Z","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":"30cbd11021b497578ebf49fb941b1e138b36041dbaff243b2e00a82763f9f7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-27T06:29:35Z","title_canon_sha256":"a136ee2ef325a1f6ffda06baf08f920520dbeb16fc678033aecf49d914a1a884"},"schema_version":"1.0","source":{"id":"1009.5168","kind":"arxiv","version":2}},"canonical_sha256":"1eb2ba5ee3519b56eb152da4f0e81d06cdba89248c6db557a6e2303ba664efd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1eb2ba5ee3519b56eb152da4f0e81d06cdba89248c6db557a6e2303ba664efd9","first_computed_at":"2026-05-18T04:22:40.270475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:40.270475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xFXVnBKDzB6i7kfvMvq2POdIrTdIhVGWGwDT11ZWq6RNOdzs1+E+HtsQsIRc1s4lqBOoTlXlHMyfc9nMdm1vBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:40.271109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5168","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f702dbfb29292b719356c58cf2a3c27d9ab5c6f6e5d5a4f87d918a9dc3691ef0","sha256:17f32b832738522e88652dc61adab78dbc18a653929255e9b014be67d4ae6387"],"state_sha256":"43e5bc232520a846984b0e2d9a2aad1dcb906bfc77cb4eff56cb8cbee5d89af5"}