{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VCWYITJVLNQNV3RF3Z4M6NOTWW","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":"5851661b3e4833d8de25ecc1851d1304b09496e30d5d72df61ba25ef6886c1e1","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-28T21:35:40Z","title_canon_sha256":"2d2237a0cf1d50a9742f0b32e7375edd0e0f74c30522f7ab293af2965ed8e95e"},"schema_version":"1.0","source":{"id":"1104.5517","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5517","created_at":"2026-05-18T03:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5517v2","created_at":"2026-05-18T03:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5517","created_at":"2026-05-18T03:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"VCWYITJVLNQN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VCWYITJVLNQNV3RF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VCWYITJV","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:a541c5438d13c720512bd8605e54ea234512bb4b549628eb0a9bfbfb4527fdd5","target":"graph","created_at":"2026-05-18T03:39:16Z","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 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","authors_text":"Amr Elmasry, J. Ian Munro, Meng He, Patrick K. Nicholson","cross_cats":["cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-28T21:35:40Z","title":"Dynamic Range Majority Data Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5517","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":"sha256:8ef095ecaa0c02057e67c381c81c1e18aea2a335199c67c9b6c9ea4f4500b579","target":"record","created_at":"2026-05-18T03:39:16Z","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":"5851661b3e4833d8de25ecc1851d1304b09496e30d5d72df61ba25ef6886c1e1","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-28T21:35:40Z","title_canon_sha256":"2d2237a0cf1d50a9742f0b32e7375edd0e0f74c30522f7ab293af2965ed8e95e"},"schema_version":"1.0","source":{"id":"1104.5517","kind":"arxiv","version":2}},"canonical_sha256":"a8ad844d355b60daee25de78cf35d3b5aec5b3600bddda88ccaaa92a44757b08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8ad844d355b60daee25de78cf35d3b5aec5b3600bddda88ccaaa92a44757b08","first_computed_at":"2026-05-18T03:39:16.866923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:16.866923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NmHYq3tEh3fDSMoIUizKt4RqBRMcD9/54J8lLVLNSD19KuHP1+NkSexNeYYMAQxOUrHXR234S2PxdUqHmKmJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:16.867485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5517","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ef095ecaa0c02057e67c381c81c1e18aea2a335199c67c9b6c9ea4f4500b579","sha256:a541c5438d13c720512bd8605e54ea234512bb4b549628eb0a9bfbfb4527fdd5"],"state_sha256":"81e35f810d800432719c41092325ac68be1fecef866996fcf4196b992a3284fc"}