Minimum linear gossip graphs and maximal linear (Δ, <i>k</i>)‐gossip graphs
Bibliographic record
Abstract
Abstract Gossiping is an information dissemination problem in which each node of a communication network has a unique piece of information that must be transmitted to all other nodes using two‐way communications between pairs of nodes along the communication links of the network. In this paper, we study gossiping using a linear‐cost model of communication which includes a start‐up time and a propagation time which is proportional to the amount of information transmitted. A minimum linear gossip graph is a graph (modeling a network), with the minimum possible number of links, in which gossiping can be completed in minimum time under the linear‐cost model. For networks with an even number of nodes, we prove that the structure of minimum linear gossip graphs is independent of the relative values of the start‐up and unit propagation times. We prove that this is not true when the number of nodes is odd. We present four infinite families of minimum linear gossip graphs. We also present minimum linear gossip graphs for all even numbers of nodes n ≤ 32 except n = 22. A linear (Δ, k)‐gossip graph is a graph with maximum degree Δ in which gossiping can be completed in k rounds with minimum propagation time. We present three infinite families of maximal linear (Δ, k)‐gossip graphs, that is, linear (Δ, k)‐gossip graphs with a maximum number of nodes. We show that not all minimum broadcast graphs are maximal linear (Δ, k)‐gossip graphs. © 2001 John Wiley & Sons, Inc.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".