Bibliographic record
Abstract
We consider broadcasting a message from one node of a tree to all other nodes. In the presence of up to k link failures the tree becomes disconnected, and only nodes in the connected component C containing the source can be informed. The maximum ratio between the time used by a broadcasting scheme B to inform C and the optimal time to inform C, taken over all components C yielded by configurations of at most k faults, is the k-vulnerability of B. This is the maximum slowdown incurred by B due to the lack of a priori knowledge of fault location, for at most k faults. Since the upper bound k on the number of faults is not always known, it is important to design broadcasting schemes that behave well under any possible number of faults. It turns out that achieving the lowest possible k-vulnerability for all k simultaneously is impossible for some trees. Hence a natural goal is to seek, for any tree T, a broadcasting scheme that simultaneously approximates the lowest possible k-vulnerability for every k, up to a given constant factor c (independent of L). We describe a polynomial algorithm which decides if such a "universally fault-tolerant" broadcasting scheme exists for given T and c, and constructs such a scheme if it exists.
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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 | 0.000 |
| 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".