{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TS7SXA356Y6I4D27G7J2J32AHX","short_pith_number":"pith:TS7SXA35","canonical_record":{"source":{"id":"1706.07719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-06-23T14:24:32Z","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"title_canon_sha256":"4551553dc794f5088b54c3405a2e1c08d35ed60392b64cbeba64b8f9b30028f9","abstract_canon_sha256":"d9665147393f9d57cd348f40c832daea27d2d53acb4692cf17270e48834dc14a"},"schema_version":"1.0"},"canonical_sha256":"9cbf2b837df63c8e0f5f37d3a4ef403ddd423308cdd945af320b1fc5abb5793f","source":{"kind":"arxiv","id":"1706.07719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07719","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07719v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07719","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"TS7SXA356Y6I","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TS7SXA356Y6I4D27","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TS7SXA35","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TS7SXA356Y6I4D27G7J2J32AHX","target":"record","payload":{"canonical_record":{"source":{"id":"1706.07719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-06-23T14:24:32Z","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"title_canon_sha256":"4551553dc794f5088b54c3405a2e1c08d35ed60392b64cbeba64b8f9b30028f9","abstract_canon_sha256":"d9665147393f9d57cd348f40c832daea27d2d53acb4692cf17270e48834dc14a"},"schema_version":"1.0"},"canonical_sha256":"9cbf2b837df63c8e0f5f37d3a4ef403ddd423308cdd945af320b1fc5abb5793f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:48.366477Z","signature_b64":"reqnoMhid8UEMQhVnXwnReC/0MAKBVzec4eL/X4OUqLDHvlQJg0mWmSoFkN5pEbtr002G7FYyF1kCO8DWiknBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cbf2b837df63c8e0f5f37d3a4ef403ddd423308cdd945af320b1fc5abb5793f","last_reissued_at":"2026-05-18T00:41:48.365812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:48.365812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.07719","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+g66VdzwGXHkt4j9ONwftsHZH15gs1k1trfNJHNVpoL8QdVNAhk9ySkQu40LXU6Pa7diVIXaWMSQx/OsLAJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:03:06.454078Z"},"content_sha256":"d608e4048e531d97f9ffcfc4e3ea620a640751140407896b85135da301f35027","schema_version":"1.0","event_id":"sha256:d608e4048e531d97f9ffcfc4e3ea620a640751140407896b85135da301f35027"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TS7SXA356Y6I4D27G7J2J32AHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Query Complexity of Clustering with Side Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Arya Mazumdar, Barna Saha","submitted_at":"2017-06-23T14:24:32Z","abstract_excerpt":"Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, \"do two elements $u$ and $v$ belong to the same cluster?\". The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we initiate a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and provide strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07719","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYU+0Lmi0X+zukCGCw8NL5msyfWhybO/KUNxuxh92dkZA/36XYGZ40x4h7P0Zc478rXuVZExroDxhHbimaJpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:03:06.454433Z"},"content_sha256":"88829aa6a50e657f4151122f9b1cfaef6165b4d15b7f57d891345663a3031b62","schema_version":"1.0","event_id":"sha256:88829aa6a50e657f4151122f9b1cfaef6165b4d15b7f57d891345663a3031b62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TS7SXA356Y6I4D27G7J2J32AHX/bundle.json","state_url":"https://pith.science/pith/TS7SXA356Y6I4D27G7J2J32AHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TS7SXA356Y6I4D27G7J2J32AHX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T10:03:06Z","links":{"resolver":"https://pith.science/pith/TS7SXA356Y6I4D27G7J2J32AHX","bundle":"https://pith.science/pith/TS7SXA356Y6I4D27G7J2J32AHX/bundle.json","state":"https://pith.science/pith/TS7SXA356Y6I4D27G7J2J32AHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TS7SXA356Y6I4D27G7J2J32AHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TS7SXA356Y6I4D27G7J2J32AHX","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":"d9665147393f9d57cd348f40c832daea27d2d53acb4692cf17270e48834dc14a","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-06-23T14:24:32Z","title_canon_sha256":"4551553dc794f5088b54c3405a2e1c08d35ed60392b64cbeba64b8f9b30028f9"},"schema_version":"1.0","source":{"id":"1706.07719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07719","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07719v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07719","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"TS7SXA356Y6I","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TS7SXA356Y6I4D27","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TS7SXA35","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:88829aa6a50e657f4151122f9b1cfaef6165b4d15b7f57d891345663a3031b62","target":"graph","created_at":"2026-05-18T00:41:48Z","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":"Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, \"do two elements $u$ and $v$ belong to the same cluster?\". The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we initiate a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and provide strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix","authors_text":"Arya Mazumdar, Barna Saha","cross_cats":["cs.DS","cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-06-23T14:24:32Z","title":"Query Complexity of Clustering with Side Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07719","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:d608e4048e531d97f9ffcfc4e3ea620a640751140407896b85135da301f35027","target":"record","created_at":"2026-05-18T00:41:48Z","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":"d9665147393f9d57cd348f40c832daea27d2d53acb4692cf17270e48834dc14a","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-06-23T14:24:32Z","title_canon_sha256":"4551553dc794f5088b54c3405a2e1c08d35ed60392b64cbeba64b8f9b30028f9"},"schema_version":"1.0","source":{"id":"1706.07719","kind":"arxiv","version":1}},"canonical_sha256":"9cbf2b837df63c8e0f5f37d3a4ef403ddd423308cdd945af320b1fc5abb5793f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cbf2b837df63c8e0f5f37d3a4ef403ddd423308cdd945af320b1fc5abb5793f","first_computed_at":"2026-05-18T00:41:48.365812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:48.365812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"reqnoMhid8UEMQhVnXwnReC/0MAKBVzec4eL/X4OUqLDHvlQJg0mWmSoFkN5pEbtr002G7FYyF1kCO8DWiknBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:48.366477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d608e4048e531d97f9ffcfc4e3ea620a640751140407896b85135da301f35027","sha256:88829aa6a50e657f4151122f9b1cfaef6165b4d15b7f57d891345663a3031b62"],"state_sha256":"547510b56e5bb8795b3ffc12be715707df16b0e3bf6152d63d40931652144872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UlDOGP2QKWgEzjxchgYhPrLc/xLyNluI59luOIr/RLYWlBYCzBsF5S0vqeiHnxkLKI+LrY1XNKL/if3ktnaVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:03:06.456391Z","bundle_sha256":"939413b294046e088cd32dfabbdbc0847b5c05cdd52e19d93ff7d13d96758598"}}