Asynchronous Gathering in a Dangerous Ring
Bibliographic record
Abstract
Consider a set of k identical asynchronous mobile agents located in an anonymous ring of n nodes. The classical Gather (or Rendezvous) problem requires all agents to meet at the same node, not a priori decided, within a finite amount of time. This problem has been studied assuming that the network is safe for the agents. In this paper, we consider the presence in the ring of a stationary process located at a node that disables any incoming agent without leaving any trace. Such a dangerous node is known in the literature as a black hole, and the determination of its location has been extensively investigated. The presence of the black hole makes it deterministically unfeasible for all agents to gather. So, the research concern is to determine how many agents can gather and under what conditions. In this paper we establish a complete characterization of the conditions under which the problem can be solved. In particular, we determine the maximum number of agents that can be guaranteed to gather in the same location depending on whether k or n is unknown (at least one must be known). These results are tight: in each case, gathering with one more agent is deterministically unfeasible. All our possibility proofs are constructive: we provide mobile agent algorithms that allow the agents to gather within a predefined distance under the specified conditions. The analysis of the time costs of these algorithms show that they are optimal. Our gathering algorithm for the case of unknown k is also a solution for the black hole location problem. Interestingly, its bounded time complexity is Θ(n); this is a significant improvement over the existing O(nlogn) bounded time complexity.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 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".