Low Space Data Structures for Geometric Range Mode Query.
Why this work is in the frame
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Bibliographic record
Abstract
Let S be a set of n points in d dimensions, such that each point is assigned a color. Given a query range Q = [a1, b1] × [a2, b2] ×... × [ad, bd], the geometric range mode query problem asks to report the most frequent color (i.e., a mode) of the multiset of colors corresponding to points in S ∩ Q. When d = 1, Chan et al. (STACS 2012 [1]) gave a data structure that requires O(n + (n/∆)2/w) words and supports range mode queries in O(∆) time for any ∆ ≥ 1, where w = Ω(log n) is the word size. Chan et al. also proposed a data structures for higher dimensions (i.e., d ≥ 2) with O(sn + (n/∆)2d) words and O( ∆ · tn) query time, where sn and tn denote the space and query time of a data structure that supports orthogonal range counting queries on the set S. In this paper we show that the space can be improved without any increase to the query time, by presenting an O(sn + (n/∆)2d/w) words data structure that supports orthogonal range mode queries on a set of n points in d dimensions in O( ∆ · tn) time, for any ∆ ≥ 1. When d = 1, these space and query time costs match those achieved by the current best known one-dimensional data structure.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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