{"paper":{"title":"Fast Leaf-to-Ancestor Minimum Query in the Oracle Model","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"A static data structure preprocesses a rooted tree in O(n log h) oracle comparisons to answer any leaf-to-ancestor minimum query in O(1) time with no comparisons at query time.","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Aleksandr Levin, Aleksey Upirvitskiy","submitted_at":"2026-05-13T20:56:02Z","abstract_excerpt":"We study leaf-to-ancestor path-minimum queries on a rooted, weighted tree in the oracle model, where the only allowed value operation is a comparison oracle on edge (or node) weights. We give a static data structure that, after O(n log h) preprocessing time, space, and oracle calls (where $n$ is the number of nodes and $h$ is the tree height), answers any leaf-to-ancestor query in O(1) worst-case time with zero oracle calls at query time. The method combines (I) an edge-to-node weight conversion with a deterministic tie-break to obtain a total order; (II) ladder (longest-path) decomposition; ("},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give a static data structure that, after O(n log h) preprocessing time, space, and oracle calls, answers any leaf-to-ancestor query in O(1) worst-case time with zero oracle calls at query time. The preprocessing oracle-comparison bound is tight in the deterministic comparison model.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The input is a rooted tree whose edge (or node) weights admit a total order via a deterministic tie-breaking rule when the comparison oracle returns equality; the oracle is consistent across all calls.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A data structure preprocesses a rooted weighted tree in O(n log h) time and space using comparisons to support O(1)-time leaf-to-ancestor minimum queries with zero oracle calls at query time.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A static data structure preprocesses a rooted tree in O(n log h) oracle comparisons to answer any leaf-to-ancestor minimum query in O(1) time with no comparisons at query time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ac1f06fca66a752bc098f50966947ec2d11d455793a90380f2bb26ef6ef10c48"},"source":{"id":"2605.14112","kind":"arxiv","version":1},"verdict":{"id":"ff91019e-6703-4c8c-a998-a8dd0d08b4b1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:51:31.411426Z","strongest_claim":"We give a static data structure that, after O(n log h) preprocessing time, space, and oracle calls, answers any leaf-to-ancestor query in O(1) worst-case time with zero oracle calls at query time. The preprocessing oracle-comparison bound is tight in the deterministic comparison model.","one_line_summary":"A data structure preprocesses a rooted weighted tree in O(n log h) time and space using comparisons to support O(1)-time leaf-to-ancestor minimum queries with zero oracle calls at query time.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The input is a rooted tree whose edge (or node) weights admit a total order via a deterministic tie-breaking rule when the comparison oracle returns equality; the oracle is consistent across all calls.","pith_extraction_headline":"A static data structure preprocesses a rooted tree in O(n log h) oracle comparisons to answer any leaf-to-ancestor minimum query in O(1) time with no comparisons at query time."},"references":{"count":3,"sample":[{"doi":"","year":2021,"title":"arXiv:2105.01864 [cs.DS] (2021).https://arxiv.org/abs/2105.01864","work_id":"cb65e55b-de28-4603-87bd-8c93a50c7b06","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/bf02526037","year":1997,"title":"Algorithmica 18, 263–270 (1997).https://doi.org/10.1007/BF02526037","work_id":"84887db8-ccb3-4d0b-99da-7b9209c58f98","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.tcs","year":2004,"title":"Robustness of temporal logic specifications for continuous-time sig- nals","work_id":"b4fc9e91-7fe2-4ebf-8b5d-fdb12379e17e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":3,"snapshot_sha256":"2f5a73ff2cd64fd5cfdd22c307f66f5fb1a5ccff03b2a37eb603e7eb9936e037","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"}