Categorical range maxima queries
Bibliographic record
Abstract
Given an array A[1...n] of n distinct elements from the set {1, 2, ..., n} a range maximum query RMQ(a, b) returns the highest element in A[a...b] along with its position. In this paper, we study a generalization of this classical problem called Categorical Range Maxima Query (CRMQ) problem, in which each element A[i] in the array has an associated category (color) given by C[i] ∈ [σ]. A query then asks to report each distinct color c appearing in C[a...b] along with the highest element (and its position) in A[a...b] with color c. Let pc denote the position of the highest element in A[a...b] with color c. We investigate two variants of this problem: a threshold version and a top-k version. In threshold version, we only need to output the colors with A[pc] more than the input threshold τ, whereas top-k variant asks for k colors with the highest A[pc] values. In the word RAM model, we achieve linear space structure along with O(k) query time, that can report colors in sorted order of A[•]. In external memory, we present a data structure that answers queries in optimal O(1+k/B) I/O's using almost-linear O(n log* n) space, as well as a linear space data structure with O(log* n + k/B) query I/Os. Here k represents the output size, log* n is the iterated logarithm of n and B is the block size. CRMQ has applications to document retrieval and categorical range reporting -- giving a one-shot framework to obtain improved results in both these problems. Our results for CRMQ not only improve the existing best known results for three-sided categorical range reporting but also overcome the hurdle of maintaining color uniqueness in the output set.
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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 | 0.003 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.017 |
| Open science | 0.005 | 0.007 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.017 | 0.003 |
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".