Finding All Breadth First Full Spanning Trees in a Directed Graph
Why this work is in the frame
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Bibliographic record
Abstract
This paper proposes an algorithm that is particularly concerned with generating all possible distinct spanning trees that are based on breadth-first-search directed graph traversal. The generated trees span all edges and vertices of the original directed graph. The algorithm starts by generating an initial tree, and then generates the rest of the trees using elementary transformations. It runs in O(E+T) time where E is the number of edges and T is the number of generated trees. In the worst-case scenario, this is equivalent to O (E+En/Nn) time complexity where N is the number of nodes in the original graph. The algorithm requires O(T) space. However, possible modifications to improve the algorithm space complexity are suggested. Furthermore, experiments are conducted to evaluate the algorithm performance and the results are listed.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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