Bibliographic record
Abstract
A t-spanner is a graph in which the shortest path between two vertices never exceeds t times the distance between the two nodes – a t-approximation of the complete graph. A geometric graph is one in which its vertices are points with defined coordinates and the edges correspond to line segments between them with a distance function, such as Euclidean distance. Geometric spanners are used to design networks of reduced complexity, optimizing metrics such as the planarity or degree of the graph. One famous algorithm used to generate spanners is path-greedy, which scans pairs of points in non-decreasing order of distance and adds the edge between them unless the current set of added edges already connects them with a path that t-approximates the edge length. Graphs from this algorithm are called path-greedy spanners. This work analyzes properties of path-greedy geometric spanners under different conditions. Specifically, we answer an open problem regarding the planarity and degree of path-greedy 5.19-spanners in convex point sets, and explore how the algorithm behaves under random tiebreaks for grid point sets. Lastly, we show a simple and efficient way to reduce the degree of a plane spanner by adding extra points.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".