A unified neighbourhood broadcasting scheme for multiple messages on interconnection networks
Bibliographic record
Abstract
The neighbourhood broadcasting problem on an interconnection network is defined as sending a fixed sized message from the source node to all its neighbours where in one time unit, a node can send to or receive from exactly one of its neighbours a datum of constant size. Previously, this problem has been studied for the hypercube, the star and the pancake interconnection networks, and a special family of Cayley graphs of permutation groups formed by transpositions. Here, we study the problem when the source node has m multiple messages (or a single message of size m). We develop a simple and novel scheme so that the neighbourhood broadcasting of m messages can be done in asymptotically optimal time of O(m +log n), where n is the degree of the source node. This scheme is a general and unified scheme in that it applies to several interconnection networks such as the hypercube, the star, and the pancake, all in the family of Cayley graphs. The scheme can be used in any regular interconnection networks with the similar cycle structure as in the aforementioned graphs.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".