Steiner type problems for digraphs that are locally semicomplete or extended semicomplete
Bibliographic record
Abstract
Abstract We consider the following three problems: (P1) LetDbe a strong digraph and letXbe a non‐empty subset of its vertices. Find a strong subdigraphD′ ofDwhich contains all vertices ofXand has as few arcs as possible. This problem is also known under the name the directed Steiner problem. (P2) LetDbe a strong digraph with real‐valued costs on the vertices. Find a strong subdigraph ofDof minimum cost. (P3) LetDbe a strong digraph with real‐valued costs on the vertices. Find a cycle of minimum cost inD. 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 setXof vertices. We describe polynomial algorithms for the problems (P1) and (P2) in the case whenDis 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 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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".