Computational study of a branching algorithm for the maximum \(k\)-cut problem
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Bibliographic record
Abstract
Abstract This work considers the graph partitioning problem known as maximum k -cut. It focuses on investigating features of a branch-and-bound method to obtain global solutions. An exhaustive experimental study is carried out for the two main components of a branch-and-bound algorithm: Computing bounds and branching strategies. In particular, we propose the use of a variable neighborhood search metaheuristic to compute good feasible solutions, the k -chotomic strategy to split the problem, and a branching rule based on edge weights to select variables. Moreover, we analyze a linear relaxation strengthened by semidefinite-based constraints, a cutting plane algorithm, and node selection strategies. Computational results show that the resulting method outperforms the state-of-the-art approach and discovers the solution of several instances, especially for problems with k ≥ 5 .
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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 | 0.000 |
| 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