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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14112 |
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| _version_ | 1866917537534443520 |
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| author | Upirvitskiy, Aleksey Levin, Aleksandr |
| author_facet | Upirvitskiy, Aleksey Levin, Aleksandr |
| contents | 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; (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14112 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast Leaf-to-Ancestor Minimum Query in the Oracle Model Upirvitskiy, Aleksey Levin, Aleksandr Data Structures and Algorithms Computational Complexity 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; (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 |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2605.14112 |