Bibliographic record
Abstract
Consider a tree T on n nodes, each having a weight drawn from [1‥σ]. In this article, we study the problem of supporting various path queries over the tree T . The path counting query asks for the number of the nodes on a query path whose weights are in a query range, while the path reporting query requires to report these nodes. The path median query asks for the median weight on a path between two given nodes, and the path selection query returns the k -th smallest weight. We design succinct data structures to encode T using n nH ( W T ) + 2 n + o ( n lg σ) bits of space, such that we can support path counting queries in O (lg σ/lg lg n + 1)) time, path reporting queries in O (( occ +1)(lg σ / lg lg n + 1)) time, and path median and path selection queries in O (lg σ / lg lg σ) time, where H ( W T ) is the entropy of the multiset of the weights of the nodes in T and occ is the size of the output. Our results not only greatly improve the best known data structures [Chazelle 1987; Krizanc et al. 2005], but also match the lower bounds for path counting, median, and selection queries [Pătraşcu 2007, 2011; Jørgensen and Larsen 2011] when σ = Ω( n /polylog( n )).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.038 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.007 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.005 | 0.024 |
| Open science | 0.005 | 0.008 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.015 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".