{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VCWYITJVLNQNV3RF3Z4M6NOTWW","short_pith_number":"pith:VCWYITJV","schema_version":"1.0","canonical_sha256":"a8ad844d355b60daee25de78cf35d3b5aec5b3600bddda88ccaaa92a44757b08","source":{"kind":"arxiv","id":"1104.5517","version":2},"attestation_state":"computed","paper":{"title":"Dynamic Range Majority Data Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DS","authors_text":"Amr Elmasry, J. Ian Munro, Meng He, Patrick K. Nicholson","submitted_at":"2011-04-28T21:35:40Z","abstract_excerpt":"Given a set $P$ of coloured points on the real line, we study the problem of answering range $\\alpha$-majority (or \"heavy hitter\") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to more than an $\\alpha$-fraction of the points contained in $Q$. We present a new data structure for answering range $\\alpha$-majority queries on a dynamic set of points, where $\\alpha \\in (0,1)$. Our data structure uses O(n) space, supports queries in $O((\\lg n) / \\alpha)$ time, and updates in $O((\\lg n) / \\alpha)$ amortized time. If the coordinates of the poi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1104.5517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-28T21:35:40Z","cross_cats_sorted":["cs.DB"],"title_canon_sha256":"2d2237a0cf1d50a9742f0b32e7375edd0e0f74c30522f7ab293af2965ed8e95e","abstract_canon_sha256":"5851661b3e4833d8de25ecc1851d1304b09496e30d5d72df61ba25ef6886c1e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:16.867485Z","signature_b64":"NmHYq3tEh3fDSMoIUizKt4RqBRMcD9/54J8lLVLNSD19KuHP1+NkSexNeYYMAQxOUrHXR234S2PxdUqHmKmJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8ad844d355b60daee25de78cf35d3b5aec5b3600bddda88ccaaa92a44757b08","last_reissued_at":"2026-05-18T03:39:16.866923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:16.866923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamic Range Majority Data Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DS","authors_text":"Amr Elmasry, J. Ian Munro, Meng He, Patrick K. Nicholson","submitted_at":"2011-04-28T21:35:40Z","abstract_excerpt":"Given a set $P$ of coloured points on the real line, we study the problem of answering range $\\alpha$-majority (or \"heavy hitter\") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to more than an $\\alpha$-fraction of the points contained in $Q$. We present a new data structure for answering range $\\alpha$-majority queries on a dynamic set of points, where $\\alpha \\in (0,1)$. Our data structure uses O(n) space, supports queries in $O((\\lg n) / \\alpha)$ time, and updates in $O((\\lg n) / \\alpha)$ amortized time. If the coordinates of the poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5517","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.5517","created_at":"2026-05-18T03:39:16.866992+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.5517v2","created_at":"2026-05-18T03:39:16.866992+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5517","created_at":"2026-05-18T03:39:16.866992+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCWYITJVLNQN","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCWYITJVLNQNV3RF","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCWYITJV","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW","json":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW.json","graph_json":"https://pith.science/api/pith-number/VCWYITJVLNQNV3RF3Z4M6NOTWW/graph.json","events_json":"https://pith.science/api/pith-number/VCWYITJVLNQNV3RF3Z4M6NOTWW/events.json","paper":"https://pith.science/paper/VCWYITJV"},"agent_actions":{"view_html":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW","download_json":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW.json","view_paper":"https://pith.science/paper/VCWYITJV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.5517&json=true","fetch_graph":"https://pith.science/api/pith-number/VCWYITJVLNQNV3RF3Z4M6NOTWW/graph.json","fetch_events":"https://pith.science/api/pith-number/VCWYITJVLNQNV3RF3Z4M6NOTWW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW/action/storage_attestation","attest_author":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW/action/author_attestation","sign_citation":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW/action/citation_signature","submit_replication":"https://pith.science/pith/VCWYITJVLNQNV3RF3Z4M6NOTWW/action/replication_record"}},"created_at":"2026-05-18T03:39:16.866992+00:00","updated_at":"2026-05-18T03:39:16.866992+00:00"}