On the Hamiltonicity, Connectivity, and Broadcasting Algorithm of the KCube
Bibliographic record
Abstract
The KCube is a newly proposed topology for connecting many processors in an interconnection or communication network. It combines the well known Kautz graph and the hypercube. The KCube is defined in such a way that it is a class of graphs that have to satisfy two conditions for a graph to be a KCube. Therefore, different versions of the KCube are possible depending on how input and output nodes (vertices) are defined. Originally, together with the definition of the KCube family, a specific version of the KCube is also presented. In this paper, we (1) propose a KCube graph that also belongs to the KCube family and is yet different from the original one, study some of the properties of our KCube, and show that it is Hamiltonian, (2) derive its connectivity, and (3) develop an optimal broadcasting algorithm. The results in (2) and (3) are for the general KCube family regardless of how input and output nodes are specified.
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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 | 0.001 | 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 | 0.000 | 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".