Near Optimal Broadcasting in Optimal Triple Loop Graphs
Bibliographic record
Abstract
Triple loop networks (graphs) are generalizations of the ring topology where every vertex v is linked to 6 vertices v a, v b, v c. In this paper, we study the broadcast problem in optimal triple loop graphs. In 1987 for a restricted case a = -(b + c) the (maximum) number of vertices in the sub- optimal Triple loop graph has been proved to be a quadratic function of diameter d. In 1998 the broadcast time of this graph is proved to be d + 3. Recently, in 2003 the Optimal Triple Loop Graph in general was constructed, where its number of vertices is a cubic function of d. In this paper we prove d + 2 lower bound and d + 5 upper bound for broadcasting in general Optimal Triple Loop Graph. We also generalize our upper bound algorithm in Multiple Loop Graphs giving d + 2 k-1 general upper bound where the degree of every vertex is 2 k.
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How this classification was reachedexpand
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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".