The Ring Star Problem: Polyhedral analysis and exact algorithm
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In the Ring Star Problem, the aim is to locate a simple cycle through a subset of vertices of a graph with the objective of minimizing the sum of two costs: a ring cost proportional to the length of the cycle and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. The problem has several applications in telecommunications network design and in rapid transit systems planning. It is an extension of the classical location–allocation problem introduced in the early 1960s, and closely related versions have been recently studied by several authors. This article formulates the problem as a mixed‐integer linear program and strengthens it with the introduction of several families of valid inequalities. These inequalities are shown to be facet‐defining and are used to develop a branch‐and‐cut algorithm. Computational results show that instances involving up to 300 vertices can be solved optimally using the proposed methodology. © 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