Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
Bibliographic record
Abstract
We consider approximation algorithms for non-uniform buy-at-bulk network design problems. The first non-trivial approximation algorithm for this problem is due to Charikar and Karagiozova (STOC 05); for an instance on h pairs their algorithm has an approximation guarantee of exp(O(radic(log h log log h)))for the uniform-demand case, and log D middot exp(O(radic(log h log log h))) for the general demand case, where D is the total demand. We improve upon this result, by presenting the first poly-logarithmic approximation for this problem. The ratio we obtain is O(log3h middot min{log D, gamma(h2)}) where his the number of pairs and gamma(n) is the worst case distortion in embedding the metric induced by a n vertex graph into a distribution over its spanning trees. Using the best known upper bound on gamma(n) we obtain an O(min{log3h middot log D, log5h log log h}) ratio approximation. We also give poly-logarithmic approximations for some variants of the single-source problem that we need for the multicommodity problem
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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 | 0.004 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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".