Bibliographic record
Abstract
Broadcasting is a data communication task in which one processor sends the same message to all other processors. Routing is a task where a source processor sends a message to a destination processor. A faulty node is in an error state and cannot participate in the activities or the communication in a given network. In this paper, we consider the family of mesh networks, which include the mesh connected computer (MCC), k-dimensional mesh, torus, and k-ary n-cube. Our goal is to design routing and broadcasting algorithms which will use local knowledge of faults, no additional resources, will work for an arbitrary number and structure of faults, will guarantee delivery to all nodes connected to the source, and will remain optimal in a fault free mesh. We did not find any solution in literature to satisfy these desirable properties. Our routing and broadcasting schemes for MCCs and tori, and our broadcasting algorithm for the all-port model on any faulty mesh network satisfy all of these properties. For routing and broadcasting in a one-port model in higher dimensions, a condition on fault structure needs to be met. We propose a new broadcasting algorithm which guarantees delivery to all processors connected to the source in the all-port model of faulty meshes. We then describe a routing algorithm that guarantees delivery in faulty MCCs and tori, the connectivity of the source and destination being the only obvious requirement. The algorithm can be extended to faulty k-D meshes and k-ary n-cubes, where the delivery will be guaranteed if healthy nodes in every 2-D submesh (sub-tori) remain connected. We then describe broadcasting algorithms for the one-port model, which again guarantee delivery to all connected processors in two-dimensional cases, and guarantee delivery in k-dimensional cases if healthy processors in every 2-D submesh (sub-tori) remain connected.
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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".