Improved algorithms for weakly chordal graphs
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Bibliographic record
Abstract
We use a new structural theorem on the presence of two-pairs in weakly chordal graphs to develop improved algorithms. For the recognition problem, we reduce the time complexity from O( mn 2 ) to O( m 2 ) and the space complexity from O( n 3 ) to O( m + n ), and also produce a hole or antihole if the input graph is not weakly chordal. For the optimization problems, the complexity of the clique and coloring problems is reduced from O( mn 2 ) to O( n 3 ) and the complexity of the independent set and clique cover problems is improved from O( n 4 ) to O( mn ). The space complexity of our optimization algorithms is O( m + n ).
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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 it