Scattered Black Hole Search in an Oriented Ring using Tokens
Why this work is in the frame
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Bibliographic record
Abstract
A black hole is a highly harmful host that disposes of visiting agents upon their arrival without any observable trace of the destruction. The problem of locating the black hole in asynchronous ring network is known to be solvable by a team of mobile agents if each node is equipped with a whiteboard. A simpler and less expensive inter-communication and synchronization mechanism is provided by tokens: each agent has available a bounded number of tokens that can be carried, placed in a node or/and on a port of the node, or removed. All tokens are identical and no other form of communication or coordination is available to the agents. It is known that locating the black hole in an anonymous ring network using tokens is feasible when the team of agents is initially collocated (i.e. they all start from the same host). Recently, the more difficult case when the agents are scattered (i.e., when the agents do not start from the same host) has also been examined and solutions requiring only O(1) tokens per agent but using a total of O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) moves have been presented. The number of moves can be reduced to O(kn + n log n) if the number k of agents is known. In this paper, we study the impact of orientation and knowledge of team size on the cost of black hole location by scattered agents with tokens. We prove that, in oriented rings, the number of moves can be reduced from O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to the optimal Theta(nlogn) using only O(1) tokens per agent, without any knowledge of the team size. This result holds even if both agents and nodes are anonymous. Interestingly, the proposed algorithm solves, with the same cost, also the leader election problem and the rendezvous problem for the scattered agents despite the presence of a BH.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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 it