A linear algorithm for finding the <i>k</i>‐broadcast center of a tree
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Bibliographic record
Abstract
Abstract The term k ‐broadcast indicates the process of disseminating a message from one vertex to all vertices of a graph in such a way that in each time unit, an informed vertex can send the message to up to k of its neighbors. The k ‐broadcast center of a graph is the set of vertices that can initiate a minimum time k ‐broadcast within the graph. We present a linear algorithm to determine the k ‐broadcast center of a given tree. From this, we obtain a linear time algorithm for finding the k ‐broadcast time of any vertex of the tree and, thus, the k ‐broadcast time of the tree itself. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009
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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 | 0.000 |
| 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