The generalized minimum spanning tree problem: Polyhedral analysis and branch‐and‐cut algorithm
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Bibliographic record
Abstract
Abstract This article presents a branch‐and‐cut algorithm for the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose vertex set is partitioned into clusters, the GMSTP consists of determining a minimum‐cost tree including exactly one vertex per cluster. Applications of the GMSTP are encountered in telecommunications. An integer linear programming formulation is presented and new classes of valid inequalities are developed, several of which are proved to be facet‐defining. A branch‐and‐cut algorithm and a tabu search heuristic are developed. Extensive computational experiments show that instances involving up to 160 or 200 vertices can be solved to optimality, depending on whether edge costs are Euclidean or random. © 2004 Wiley Periodicals, Inc.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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