p-cycle network design: From fewest in number to smallest in size
Bibliographic record
Abstract
An idea seems to have spread that p-cycle networks are always based on a single Hamiltonian cycle. The correct understanding is that while they can be based on a Hamiltonian, network designs involving multiple p-cycles are far more capacity-efficient in general. In fact, from an optical networking standpoint one would probably like to work with p-cycles of the smallest size (circumference) possible, to satisfy optical reach considerations, and in this case the number of p-cycles might be even more numerous than a pure minimum capacity design. However, the fact that an entire network could be protected by a single cyclic structure could be attractive from another viewpoint simply because only one logical structure has to be managed. Thus, different recent orientations have brought us to realize the need for a study of p-cycle network designs that vary systematically across the range between the smallest size p-cycles, to using the fewest number of p-cycles. Questions include: What are the design models for p-cycle networks that use the fewest number of distinct structures? What are the capacity implications of a design restricted to a specific maximum number of structures? Can a capacity-optimal design be ¿nudged¿ into using fewer structures in total without requiring any extra capacity? What happens to the number of structures if the smallest possible p-cycles are insisted upon? Accordingly, we offer a systematic study of the optimal p-cycle network design problem addressing such questions about how the logical number of p-cycle structures present or allowed in a design interacts with the minimum spare capacity required for the design to be 100% restorable.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".