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  "path": "/abs/2605.14112v1",
  "publishedAt": "2026-05-15T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Aleksey Upirvitskiy",
    "Aleksandr Levin"
  ],
  "textContent": "**Authors:** Aleksey Upirvitskiy, Aleksandr Levin\n\nWe 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; (III) binary lifting; and (IV) sparse-table RMQ built over ladder arrays, storing indices selected via the oracle during preprocessing. We also show that the preprocessing oracle-comparison bound is tight in the deterministic comparison model.",
  "title": "Fast Leaf-to-Ancestor Minimum Query in the Oracle Model"
}