A Min-Max Optimization Problem on Traffic Grooming in WDM Optical Networks
Bibliographic record
Abstract
In SONET/WDM networks, a wavelength channel is shared by multiplexed low-rate traffic demands. The multiplexing/de-multiplexing is known as traffic grooming and performed by SONET add-drop multiplexers (SADM). The grooming factor, denoted by k, is the maximum number of low-rate traffic demands that can be multiplexed in one wavelength. Since SADMs are expensive, a key optimization problem in traffic grooming is to minimize the total number of required SADMs to satisfy the full connectivity for a given set of traffic demands. In this paper, we study traffic grooming from a different point of view. We consider a Min-Max optimization problem to minimize the number of SADMs at the network node where the number of required SADMs is the maximum over all nodes. We focus on the unidirectional path-switched ring networks with arbitrary duplex traffic demands. We prove the NP-hardness of this min-max optimization problem, and propose a linear time (k+1/2 + 2)-approximation algorithm. We then show that the approximation algorithm achieves the worst case lower bound. We also study the all-to-all traffic pattern, and propose an algorithm achieving solutions only a constant factor away from the optimal ones. Extensive simulations are conducted as well to validate the performance of our algorithm.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".