Steiner type problems for digraphs that are locally semicomplete or extended semicomplete
Bibliographic record
Abstract
Abstract We consider the following three problems: (P1) Let D be a strong digraph and let X be a non‐empty subset of its vertices. Find a strong subdigraph D ′ of D which contains all vertices of X and has as few arcs as possible. This problem is also known under the name the directed Steiner problem. (P2) Let D be a strong digraph with real‐valued costs on the vertices. Find a strong subdigraph of D of minimum cost. (P3) Let D be a strong digraph with real‐valued costs on the vertices. Find a cycle of minimum cost in D . All three problems are NP‐hard for general digraphs. The second problem generalizes the problem of finding a smallest strong subdigraph (measured in the number of vertices) which covers a given non‐empty set X of vertices. We describe polynomial algorithms for the problems (P1) and (P2) in the case when D is either locally semicomplete or extended semicomplete and for (P3) in the case of locally semicomplete digraphs. A polynomial algorithm for (P3) in the case of extended semicomplete digraphs was given by Bang‐Jensen et al., 2002 . © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 193–207, 2003
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How this classification was reachedexpand
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 | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".