Window Queries On Planar Subdivisions Arising From Overlapping Polygons
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Bibliographic record
Abstract
We present ecient algorithms for partitioning 2dimensional space into faces arising from the boundaries of overlapping polygons. In particular, we examine the case where the partitioning arises from overlaying m k-sided simple polygons. A dynamic data structure is presented for storing the partitioning that arises from m polygons with at most k sides each in space O(km 2 ) if the polygons are assumed to be convex, and space O(k 2 m 2 ) for simple polygons. Our structure returns T distinct regions from an axis-aligned orthogonal range search in worst case O(mk + (m + k)(logmk)T ) time, and can be updated in O(k 2 m 2 ) time.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| 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