Scalable Design of p-Cycles for Node Protection without Candidate Pre-Enumeration
Bibliographic record
Abstract
The problem of the design of p-cycles in WDM mesh networks under single link failure scenario has been extensively investigated; however, there are very fewer studies upon the design of p-cycles for protecting against a single node failure. In this paper, we develop a new scalable design approach for calculating p-cycles with node protection capability. Conventional design methods formulate the problem as an Integer Linear Program (ILP). To solve the ILP, the prerequisite is the enumeration of all possible cycle candidates in a network. As the number of cycles increases exponentially with the increase of the network size, these methods suffer from the scalability issue. We propose a new design and solution method based on large scale optimization tools, namely Column Generation (CG), where p-cycles are generated on the fly when needed and embedded in the optimization process. The main advantage of our CG-based method is that no p-cycles are a-priori off-line enumerated; the generation of the promising set of p-cycles is embedded in the optimization process. We have carried out intensive experiments on several network instances for comparing our method with an existing method in the literature. Numerical results show that our CG-based method outperforms the previous method in terms of scalability. As it is important for Internet service providers, we also compare the spare capacity requirement of p-cycles for link and node protection with that for link protection.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".