Survivability of lightwave networks – path lengths in WDM protection scheme
Bibliographic record
Abstract
In the protection scheme of fault management in a WDM optical network, corresponding to every source‐destination path used for data transmission, a backup path is maintained in a stand‐by mode. In the case of a failure (either due to a fiber cut or due to equipment failure) in the primary path, data transmission is quickly switched to the backup path. In order to tolerate any single fault, the backup path must be edge (or node) disjoint from the primary path. Most often a shortest path between the source and the destination is chosen as the primary path. To obtain a link (node) disjoint backup (or secondary) path, the links (nodes) of the primary path are removed from the graph and then a shortest path in the modified graph is chosen as the backup path. The attractive feature of this scheme is its simplicity. However, the scheme has a severe drawback. Due to the choice of a shortest path as the primary path, the length of a link disjoint secondary path may be unacceptably large. In this paper, we propose a novel way of choosing the primary and the secondary paths so that the lengths of both the paths are small. Unfortunately, the problem of choosing primary and secondary paths in this way turns out to be NP‐complete. We provide the NP‐completeness proof of both the edge disjoint and the node disjoint version of the problem. We provide an approximation algorithm for the problem with a guaranteed performance bound of 2 and a mathematical programming formulation for the exact solution of the problem. Though the approximate solution provides a performance bound of 2, through extensive experimental evaluation, we find that the approximate solution is very close to the optimal solution and the ratio between the approximate to the optimal solution never exceeds 1.2. Although we discuss the single fault scenario in this paper, the algorithms discussed here, can be used equally effectively for the multiple fault scenario also. Finally, we discuss other variations of the disjoint path problem relevant to the lightwave networks.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| 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".