Planar Case of the Maximum Box and Related Problems
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Bibliographic record
Abstract
Given two finite sets of points X + and X − in R d ,t he maximum box problem is the problem of finding a box (hyperrectangle) B = {x : l ≤ x ≤ u} such that B ∩ X − = ∅, and the cardinality of B ∩ X + is maximized. The maximum bichromatic discrepancy problem is to find a box B maximizing the difference between the number of the points of X + and X − inside the box, i.e. max ||B ∩ X + |−| B ∩ X − ||. In this paper, we discuss an exact algorithm for the maximum box problem on the plane. In addition, we provide factor 2 approximation algorithms for planar cases of both problems and give an extension to the numerical discrepancy problem.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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