Exact solution of the centralized network design problem on directed graphs
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Bibliographic record
Abstract
Abstract We present a novel exact solution method for the centralized network design problem on directed graphs. The problem is modeled as the well‐known graph theoretic problem: the capacitated directed spanning tree problem. We propose a Lagrangian relaxation where the subproblem is a directed spanning tree with a degree constraint on the root. The master problem has an exponential number of constraints and variables. To solve it, we present a cut‐and‐column generation algorithm based on analytic centers. The latter solves a restricted master problem using a primal analytic center cutting plane method and strengthens the bound by generating columns that correspond to violated primal constraints. The Lagrangian bound is embedded within branch‐and‐bound leading to an interior point branch‐and‐price algorithm with cut generation. We use a dual interior point method to warm start the solution of the restricted master problem both after adding columns and after branching. We present numerical results indicating that the proposed approach outperforms the literature on the directed case. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(4), 181–192 2005
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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