Approximate Orthogonal Range Search using Patricia Tries
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Bibliographic record
Abstract
We use Patricia tries to answer 2-approximate orthogonal range search on a set of n random points and rectangles in k-dimensional space. Given n k-dimensional random points or rectangles and a k-dimensional query rectangle, 2-approximate orthogonal range query counts (or reports) the points in the query rectangle or the rectangles intersecting the query rectangle, allowing errors near the boundary of the query rectangle. Points within a distance of a function of 2 the boundary of the query rectangle might be misclassified. The approximate orthogonal range search time using Patricia tries is determined theoretically to be O(k log n/2k−1) for cubical range queries. Patricia tries are evaluated experimentally for 2-approximate orthogonal range counting and reporting queries (for 2 ≤ k ≤ 10 and n up to 1,000,000) using uniformly distributed random points and rectangles, and we compared the performance of the Patricia trie for k-d points with the k-d tree and the adaptive k-d tree. The experimental results show that allowing small errors can significantly improve the query execution time of the approximate range counting. For epsilon = 0.05, an average of 50% fewer nodes are visited for the Patricia trie (compared to the exace range search).
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it