{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7ISH366CXN7IHCCKZY4WIPDYFG","short_pith_number":"pith:7ISH366C","canonical_record":{"source":{"id":"1610.08543","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-10-26T20:40:09Z","cross_cats_sorted":[],"title_canon_sha256":"f132cab35b52258886cbbd44ca4e9ee2b192457aa05d2022333c2f3f57254f02","abstract_canon_sha256":"e6be62908232c4666663257711d22ab0edf921b82f6482cb5067eec423c00ce9"},"schema_version":"1.0"},"canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","source":{"kind":"arxiv","id":"1610.08543","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08543","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08543v7","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08543","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"7ISH366CXN7I","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7ISH366CXN7IHCCK","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7ISH366C","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7ISH366CXN7IHCCKZY4WIPDYFG","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08543","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-10-26T20:40:09Z","cross_cats_sorted":[],"title_canon_sha256":"f132cab35b52258886cbbd44ca4e9ee2b192457aa05d2022333c2f3f57254f02","abstract_canon_sha256":"e6be62908232c4666663257711d22ab0edf921b82f6482cb5067eec423c00ce9"},"schema_version":"1.0"},"canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.810655Z","signature_b64":"lcX+Ume+R/oSk+xlM/r37ClTRwAukwgLzqY2X225pqTZnQfi0WPBT67X/Woqm4jQleiKDY2RIPQE74CbKti5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","last_reissued_at":"2026-05-17T23:46:55.810202Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.810202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08543","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xPfCjDvktq2EFazC4Ya5F8kZo6JpN+jIy3BZcGHxmCniMbwO7VFKqeSsGsSLfJwVPTDxC4XVIMDkIYkki5QBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:55:51.420820Z"},"content_sha256":"bee3f822f4f1efe3eaea997692abccc4e7aff41058618d9942a62e0641cdcfe5","schema_version":"1.0","event_id":"sha256:bee3f822f4f1efe3eaea997692abccc4e7aff41058618d9942a62e0641cdcfe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7ISH366CXN7IHCCKZY4WIPDYFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient approximation for point-set diameter in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ali Mohades, Mahdi Imanparast, Seyed Naser Hashemi","submitted_at":"2016-10-26T20:40:09Z","abstract_excerpt":"In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\\varepsilon)$-approximation algorithm with $O(n+ 1/\\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \\varepsilon\\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\\varepsilon))$-approximation algorithm with $O(n+ 1/\\varepsilon^{\\frac{2d}{3}-\\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08543","kind":"arxiv","version":7},"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":"2026-05-17T23:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F4F2GcHuYx6q3jdNKrtUJMVWyfd2mxNuF33hiKxa6Jiv+NTkzesaAc10behJFp5kJbqMO6NWdMWcFrH2cEsiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:55:51.421616Z"},"content_sha256":"49e1f792d02efa021b080f614bcb6c48e431b9245bd1cda4e3af8349331f498a","schema_version":"1.0","event_id":"sha256:49e1f792d02efa021b080f614bcb6c48e431b9245bd1cda4e3af8349331f498a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/bundle.json","state_url":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ISH366CXN7IHCCKZY4WIPDYFG/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":"2026-05-31T10:55:51Z","links":{"resolver":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG","bundle":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/bundle.json","state":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ISH366CXN7IHCCKZY4WIPDYFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7ISH366CXN7IHCCKZY4WIPDYFG","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":"e6be62908232c4666663257711d22ab0edf921b82f6482cb5067eec423c00ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-10-26T20:40:09Z","title_canon_sha256":"f132cab35b52258886cbbd44ca4e9ee2b192457aa05d2022333c2f3f57254f02"},"schema_version":"1.0","source":{"id":"1610.08543","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08543","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08543v7","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08543","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"7ISH366CXN7I","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7ISH366CXN7IHCCK","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7ISH366C","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:49e1f792d02efa021b080f614bcb6c48e431b9245bd1cda4e3af8349331f498a","target":"graph","created_at":"2026-05-17T23:46:55Z","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":"In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\\varepsilon)$-approximation algorithm with $O(n+ 1/\\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \\varepsilon\\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\\varepsilon))$-approximation algorithm with $O(n+ 1/\\varepsilon^{\\frac{2d}{3}-\\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure.","authors_text":"Ali Mohades, Mahdi Imanparast, Seyed Naser Hashemi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-10-26T20:40:09Z","title":"An efficient approximation for point-set diameter in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08543","kind":"arxiv","version":7},"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:bee3f822f4f1efe3eaea997692abccc4e7aff41058618d9942a62e0641cdcfe5","target":"record","created_at":"2026-05-17T23:46:55Z","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":"e6be62908232c4666663257711d22ab0edf921b82f6482cb5067eec423c00ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-10-26T20:40:09Z","title_canon_sha256":"f132cab35b52258886cbbd44ca4e9ee2b192457aa05d2022333c2f3f57254f02"},"schema_version":"1.0","source":{"id":"1610.08543","kind":"arxiv","version":7}},"canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","first_computed_at":"2026-05-17T23:46:55.810202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.810202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lcX+Ume+R/oSk+xlM/r37ClTRwAukwgLzqY2X225pqTZnQfi0WPBT67X/Woqm4jQleiKDY2RIPQE74CbKti5BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.810655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08543","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bee3f822f4f1efe3eaea997692abccc4e7aff41058618d9942a62e0641cdcfe5","sha256:49e1f792d02efa021b080f614bcb6c48e431b9245bd1cda4e3af8349331f498a"],"state_sha256":"e8fd1154caa530237b64d61357c7da16612f41790e7f86b293199ac656e9040d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwd+FqhmFzcwBfmDbdIRSb/OR3k57anLmwj0CvEUhHjGgJ+eM4Ci3W3MRcFaP4ASQr2F+/PQ6MJqZR5tztvqDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:55:51.425824Z","bundle_sha256":"176b2513c67c86e98632d8fda173612dea1ca8d339e1f938e77cd59660febd8b"}}