An Algorithm for the MaxMin Area Triangulation of a Convex Polygon
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Bibliographic record
Abstract
Given a convex polygon in the plane, we are interested in triangulations of its interior, i.e. maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest area triangle in the triangulation. There exists a dynamic programming algorithm that computes the optimal triangulation with respect to a number of optimality criteria in Θ(n 3 ) time and Θ(n 2 ) space, [4]. We present an algorithm that constructs the MaxMin area triangulation of a convex polygon in O(n 2 log n log log n) time and O(n 2 ) space. The algorithm is based on the dynamic programming approach and uses a number of problem-specific geometric properties that are established within the paper.
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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 | 0.001 | 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 | 0.000 | 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