Wavelength assignment on bounded degree trees of rings
Bibliographic record
Abstract
A fundamental problem in computer and communication networks is the wavelength assignment (WA) problem: given a set of routing paths on a network, assign wavelengths (channels) to the paths such that the paths with the same wavelength are edge-disjoint. The optimization problem here is to minimize the number of wavelengths. A popular network topology is a tree of rings. It is known NP-hard to find the minimum number of wavelengths for the WA problem on a tree of rings. Let L be the maximum number of paths on any edge in the network. Then L is a lower bound on the number of wavelengths for the WA problem. We give a polynomial time algorithm which uses at most 3L wavelengths for the WA problem on a tree of rings with node degree at most eight. This improves the previous result of 4L. We also show that some instances of the WA problem require at least 3L wavelengths on a tree of rings, implying that the 3L upper bound is optimal for the worst case instances. In addition, we prove that our algorithm has approximation ratios 2 and 2.5 for a tree of rings with node degrees at most four and six, respectively.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".