A new optimal algorithm for outerplanar graph testing.
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Bibliographic record
Abstract
A graph is a mathematical abstraction that is useful in solving a variety of problems. NP-complete (Non-deterministic Polynomial) problems are computational problems for which there is no known polynomial time algorithm solving them. Unfortunately, many important graph theoretic problems are known to be NP-Complete for arbitrary graph. However, for some classes of graphs, polynomial time algorithms have been discovered. Owing to this reason, it is of both theoretical and practical interest to be able to tell if a given graph belongs to one of those classes. As a result, graph recognition has received considerable attention over the last few decades. It is well known that the Hamiltonian cycle problem is NP-Complete. However, for the class of outerplanar graphs, polynomial time algorithms for the Hamiltonian cycle problem have been proposed. In this thesis, we shall first study existing outerplanarity testing algorithms, and present a new outerplanarity testing algorithm which is optimal and much simpler than existing algorithms. The new algorithm proposed in this thesis is based on the depth-first search, an ear decomposition technique and a vertex/edge absorb operation. It is conceptually simple and is easy to implement. A rigorous proof for the correctness of the new algorithm is presented and its time complexity is analyzed.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .L56. Source: Masters Abstracts International, Volume: 43-05, page: 1753. Adviser: Y. H. Tsin. Thesis (M.Sc.)--University of Windsor (Canada), 2004.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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