Bibliographic record
Abstract
We consider a fault-tolerant generalization of the classical uncapacitated facility location problem, where each client j has a requirement that r j distinct facilities serve it, instead of just one. We give a 2.076-approximation algorithm for this problem using LP rounding, which is currently the best-known performance guarantee. Our algorithm exploits primal and dual complementary slackness conditions and is based on clustered randomized rounding . A technical difficulty that we overcome is the presence of terms with negative coefficients in the dual objective function, which makes it difficult to bound the cost in terms of dual variables. For the case where all requirements are the same, we give a primal-dual 1.52-approximation algorithm. We also consider a fault-tolerant version of the k -median problem. In the metric k -median problem, we are given n points in a metric space. We must select k of these to be centers, and then assign each input point j to the selected center that is closest to it. In the fault-tolerant version we want j to be assigned to r j distinct centers. The goal is to select the k centers so as to minimize the sum of assignment costs. The primal-dual algorithm for fault-tolerant facility location with uniform requirements also yields a 4-approximation algorithm for the fault-tolerant k -median problem for this case. This the first constant-factor approximation algorithm for the uniform requirements case.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".