How Asynchrony Affects Rumor Spreading Time
Bibliographic record
Abstract
In standard randomized (push-pull) rumor spreading, nodes communicate in synchronized rounds. In each round every node contacts a random neighbor in order to exchange the rumor (i.e., either push the rumor to its neighbor or pull it from the neighbor). A natural asynchronous variant of this algorithm is one where each node has an independent Poisson clock with rate 1, and every node contacts a random neighbor whenever its clock ticks. This asynchronous variant is arguably a more realistic model in various settings, including message broadcasting in communication networks, and information dissemination in social networks. In this paper we study how asynchrony affects the rumor spreading time, that is, the time before a rumor originated at a single node spreads to all nodes in the graph. Our first result states that the asynchronous push-pull rumor spreading time is asymptotically bounded by the standard synchronous time. Precisely, we show that for any graph G on n-nodes, where the synchronous push-pull protocol informs all nodes within T(G) rounds with high probability, the asynchronous protocol needs at most time O(T(G)+log n) to inform all nodes with high probability. On the other hand, we show that the expected synchronous push-pull rumor spreading time is bounded by O(√ n) times the expected asynchronous time. These results improve upon the bounds for both directions shown recently by Acan et al. (PODC 2015). An interesting implication of our first result is that in regular graphs, the weaker push-only variant of synchronous rumor spreading has the same asymptotic performance as the synchronous push-pull algorithm.
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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 | 0.005 | 0.066 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| 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".