Formulations and exact solution approaches for the degree preserving spanning tree problem
Bibliographic record
Abstract
Given a connected and undirected graph G, the degree preserving spanning tree problem (DPSTP) asks for a spanning tree of G with the maximum number of vertices having the same degree in the tree and in G. These are called full degree vertices. We introduce integer programming formulations, valid inequalities and four exact solution approaches based on different formulations. Two branch‐and‐bound procedures, a branch‐and‐cut (BC) algorithm and an iterative probing combinatorial Benders decomposition method are introduced here. The problem of optimally lifting one of the classes of valid inequalities proposed here is equivalent to solving a DPSTP instance, for a conveniently defined subgraph of G. We thus apply one of the proposed methods to optimally lift these cuts, within the other solution methods. In doing so, two additional algorithms, a hybrid Benders decomposition and a hybrid BC are proposed. Extensive computational experiments are conducted with the solution algorithms introduced in this study. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 329–343 2015
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".