A Lagrangean decomposition approach for the routing and wavelength assignment in multifiber WDM networks
Bibliographic record
Abstract
This paper addresses the problem of routing and wavelength assignment (RWA) in multifiber WDM networks assuming neither a special topology nor wavelength converters. Given a set of connection requests, the number of fibers deployed on each link, and the number of wavelengths a fiber can support, we seek to maximize the number of lightpaths that can be established. We formulate the problem as an integer linear program (ILP), whose validity is proven by showing that the selected lightpaths can indeed be realized by properly configuring the optical switches. Furthermore, using a Lagrangean decomposition approach, the problem formulation is significantly simplified. The main advantage of our approach is that, independent of the number of wavelengths, provably optimal solutions to the problem can be obtained by considering only one wavelength in the formulation, leading to highly efficient and scalable algorithms. Although our formulation is path-flow based rather than link-flow based, we prove that, even if all, possibly exponentially many, paths are considered, its linear programming (LP) relaxation can always be solved in polynomial time. We use the branch-and-bound algorithm in the CPLEX optimization package to solve the resulting ILP formulation. Computational results confirm the high efficiency of the Lagrangean decomposition approach.
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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 | 0.002 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".