{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:D4QJDMLMIYX2C63VRXJNTTLSS7","short_pith_number":"pith:D4QJDMLM","canonical_record":{"source":{"id":"1808.03566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-10T14:35:38Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"b8c2689af83ddcb9963c513e70ac0c39c738c9bcd35fb833dc6354865436c1ce","abstract_canon_sha256":"556b1b228e3e13aba5b4234f5cf7e48ad09144b008b202c3197cd4d9549bc7c9"},"schema_version":"1.0"},"canonical_sha256":"1f2091b16c462fa17b758dd2d9cd7297d07756fa31be7581ee8e0998807b8652","source":{"kind":"arxiv","id":"1808.03566","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03566","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03566v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03566","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"D4QJDMLMIYX2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4QJDMLMIYX2C63V","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4QJDMLM","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:D4QJDMLMIYX2C63VRXJNTTLSS7","target":"record","payload":{"canonical_record":{"source":{"id":"1808.03566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-10T14:35:38Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"b8c2689af83ddcb9963c513e70ac0c39c738c9bcd35fb833dc6354865436c1ce","abstract_canon_sha256":"556b1b228e3e13aba5b4234f5cf7e48ad09144b008b202c3197cd4d9549bc7c9"},"schema_version":"1.0"},"canonical_sha256":"1f2091b16c462fa17b758dd2d9cd7297d07756fa31be7581ee8e0998807b8652","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.641924Z","signature_b64":"lwiqEiH6ktLl5uxqSRsFLBCeEWJpZjbc6pZXFF8fAoRco6qQrfHthSl6Ecw/JiKJMNO1bvTZxp4qQmwcf0znDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f2091b16c462fa17b758dd2d9cd7297d07756fa31be7581ee8e0998807b8652","last_reissued_at":"2026-05-18T00:08:24.641299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.641299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.03566","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuykfPc+82b36i29RyCUSDbONfLHBFAI7vGC9cLZBlj90xM+Et/RsV6YDFLUUpaqcicGbcJk0DwI2tyM5vW/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:55:59.298843Z"},"content_sha256":"36ab199b961ebdc6cb79d916bcab6f5258eb5f495ac9329c8d37cea4eefd9101","schema_version":"1.0","event_id":"sha256:36ab199b961ebdc6cb79d916bcab6f5258eb5f495ac9329c8d37cea4eefd9101"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:D4QJDMLMIYX2C63VRXJNTTLSS7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greedy Algorithms for Approximating the Diameter of Machine Learning Datasets in Multidimensional Euclidean Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Ahmad B. Hassanat","submitted_at":"2018-08-10T14:35:38Z","abstract_excerpt":"Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension, so the time complexity grows exponentially in most cases, which makes these algorithms impractical. Therefore, we implemented 4 simple greedy algorithms to be used for approximating the diameter of a multidimensional dataset; these are based on minimum/maximum l2 norms, hill climbing search, Tabu search and Beam search approaches, respectively. The time comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03566","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7RQvdsmbD0Xjnlzbt0jzFQJq3VufUxEPPl30vlzmRvo5+OXvi4SAJ926aogR9i3uwkEdwfPTiKTW9JSJFo8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:55:59.299201Z"},"content_sha256":"ae251817158bcd6aaacca417e8508530c9c2f5b05a5e723b5cc026bbc26a7d85","schema_version":"1.0","event_id":"sha256:ae251817158bcd6aaacca417e8508530c9c2f5b05a5e723b5cc026bbc26a7d85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4QJDMLMIYX2C63VRXJNTTLSS7/bundle.json","state_url":"https://pith.science/pith/D4QJDMLMIYX2C63VRXJNTTLSS7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4QJDMLMIYX2C63VRXJNTTLSS7/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":"2026-06-23T19:55:59Z","links":{"resolver":"https://pith.science/pith/D4QJDMLMIYX2C63VRXJNTTLSS7","bundle":"https://pith.science/pith/D4QJDMLMIYX2C63VRXJNTTLSS7/bundle.json","state":"https://pith.science/pith/D4QJDMLMIYX2C63VRXJNTTLSS7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4QJDMLMIYX2C63VRXJNTTLSS7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:D4QJDMLMIYX2C63VRXJNTTLSS7","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":"556b1b228e3e13aba5b4234f5cf7e48ad09144b008b202c3197cd4d9549bc7c9","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-10T14:35:38Z","title_canon_sha256":"b8c2689af83ddcb9963c513e70ac0c39c738c9bcd35fb833dc6354865436c1ce"},"schema_version":"1.0","source":{"id":"1808.03566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03566","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03566v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03566","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"D4QJDMLMIYX2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D4QJDMLMIYX2C63V","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D4QJDMLM","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:ae251817158bcd6aaacca417e8508530c9c2f5b05a5e723b5cc026bbc26a7d85","target":"graph","created_at":"2026-05-18T00:08:24Z","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":"Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension, so the time complexity grows exponentially in most cases, which makes these algorithms impractical. Therefore, we implemented 4 simple greedy algorithms to be used for approximating the diameter of a multidimensional dataset; these are based on minimum/maximum l2 norms, hill climbing search, Tabu search and Beam search approaches, respectively. The time comp","authors_text":"Ahmad B. Hassanat","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-10T14:35:38Z","title":"Greedy Algorithms for Approximating the Diameter of Machine Learning Datasets in Multidimensional Euclidean Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03566","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":"sha256:36ab199b961ebdc6cb79d916bcab6f5258eb5f495ac9329c8d37cea4eefd9101","target":"record","created_at":"2026-05-18T00:08:24Z","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":"556b1b228e3e13aba5b4234f5cf7e48ad09144b008b202c3197cd4d9549bc7c9","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-10T14:35:38Z","title_canon_sha256":"b8c2689af83ddcb9963c513e70ac0c39c738c9bcd35fb833dc6354865436c1ce"},"schema_version":"1.0","source":{"id":"1808.03566","kind":"arxiv","version":1}},"canonical_sha256":"1f2091b16c462fa17b758dd2d9cd7297d07756fa31be7581ee8e0998807b8652","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f2091b16c462fa17b758dd2d9cd7297d07756fa31be7581ee8e0998807b8652","first_computed_at":"2026-05-18T00:08:24.641299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.641299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lwiqEiH6ktLl5uxqSRsFLBCeEWJpZjbc6pZXFF8fAoRco6qQrfHthSl6Ecw/JiKJMNO1bvTZxp4qQmwcf0znDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.641924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ab199b961ebdc6cb79d916bcab6f5258eb5f495ac9329c8d37cea4eefd9101","sha256:ae251817158bcd6aaacca417e8508530c9c2f5b05a5e723b5cc026bbc26a7d85"],"state_sha256":"febd93ece4a9f834328d0b364d7ee1e3f6964670cc7140e887240f9eb20c2f15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ManJ/HsPDm6jNFP2bQEPszFlKMmigfmwUqEHDxeAUQRGlppaQO9U9LhNUggbis38tsxgvSVVemc7KkuiQvIKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:55:59.301195Z","bundle_sha256":"2b8170edf911d4e0fe5d94bd547f6ad201da9b2b111a24e6937e4435992a9681"}}