Competitive Routing on a Bounded-Degree Plane Spanner
Bibliographic record
Abstract
We show that it is possible to route locally and com-petitively on two bounded-degree plane 6-spanners, one with maximum degree 12 and the other with maximum degree 9. Both spanners are subgraphs of the empty equilateral triangle Delaunay triangulation. First, in a weak routing model where the only information stored at each vertex is its neighbourhood, we show how to find a path between any two vertices of a 6-spanner of max-imum degree 12, such that the path has length at most 95/ √ 3 times the straight-line distance between the ver-tices. In a slightly stronger model, where in addition to the neighbourhood of each vertex, we store O(1) addi-tional information, we show how to find a path that has length at most 15/ √ 3 times the Euclidean distance both in a 6-spanner of maximum degree 12 and a 6-spanner of maximum degree 9.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".