Decontamination of chordal rings and tori
Bibliographic record
Abstract
In this paper we consider the problem of decontaminating a network, i.e., protecting it from unwanted and dangerous intrusions. Initially all nodes are contaminated and a team of agents is deployed to clean the entire network. When an agent transits on a node, it can clean it, when the node is left unguarded, however, it will be recontaminated as soon as at least one of its neighbour is contaminated. We study the problem in asynchronous chordal ring networks with n nodes and chord lengths d1 = 1, d2, ..., dk, and in tori. \n \nWe consider two variations of the model: one where an agent has only local knowledge, the other in which it has "visibility", i.e., it can "see" the state of its neighbouring nodes. \n \nWe first show that, when the largest chord dk is not too large (dk ≤ √n), the number of agents necessary to perform the task in chordal rings does not depend on the size of the network but only on the length of the longest chord. We also show a lower bound on the number of agents for the torus topology. We then propose tight strategies for decontamination. We analyse the number of moves and the time complexity of the decontamination algorithms showing that the visibility assumption allows us to decrease substantially both complexity measures. Another advantage of the "visibility model" is that agents move independently and autonomously without requiring any coordination.
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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".