Windrose Planarity
Bibliographic record
Abstract
Given a planar graph G and a partition of the neighbors of each vertex v in four sets v ↗ , v ↖ , v ↙ , and v ↘ , the problem W indrose P lanarity asks to decide whether G admits a windrose-planar drawing , that is, a planar drawing in which (i) each neighbor u ∈ v ↗ v is above and to the right of v , (ii) each neighbor u ∈ v ↖ is above and to the left of v , (iii) each neighbor u ∈ v ↙ is below and to the left of v , (iv) each neighbor u ∈ v ↘ is below and to the right of v , and (v) edges are represented by curves that are monotone with respect to each axis. By exploiting both the horizontal and the vertical relationship among vertices, windrose-planar drawings allow us to simultaneously visualize two partial orders defined by means of the edges of the graph. Although the problem is NP -hard in the general case, we give a polynomial-time algorithm for testing whether there exists a windrose-planar drawing that respects a given combinatorial embedding. This algorithm is based on a characterization of the plane triangulations admitting a windrose-planar drawing. Furthermore, for any embedded graph with n vertices that has a windrose-planar drawing, we can construct one with at most one bend per edge and with at most 2 n −5 bends in total, which lies on the 3 n × 3 n grid. The latter result contrasts with the fact that straight-line windrose-planar drawings may require exponential area.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 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".