Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location
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Bibliographic record
Abstract
This paper studies multilevel uncapacitated p-location problems, a general class of facility location problems. We use a combinatorial representation of the general problem where the objective function satisfies the submodular property, and we exploit this characterization to derive worst-case bounds for a greedy heuristic. We also obtain sharper bounds when the setup cost for opening facilities is zero and the allocation profits are nonnegative. Moreover, we introduce a mixed integer linear programming formulation for the problem based on the submodularity property. We present results of computational experiments to assess the performance of the greedy heuristic and that of the formulation. We compare the models with previously studied formulations. The online supplement and data are available at https://doi.org/10.1287/ijoc.2017.0757 .
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it