Generalizing the improved run-time complexity algorithm for non-dominated sorting
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Bibliographic record
Abstract
This paper generalizes the "Improved Run-Time Complexity Algorithm for Non-Dominated Sorting" by Jensen, removing its limitation that no two solutions can share identical values for any of the problem's objectives. This constraint is especially limiting for discrete combinatorial problems, but can also lead the Jensen algorithm to produce incorrect results even for problems that appear to have a continuous nature, but for which identical objective values are nevertheless possible. Moreover, even when values are not meant to be identical, the limited precision of floating point numbers can sometimes make them equal anyway. Thus a fast and correct algorithm is needed for the general case. The paper shows that generalizing the Jensen algorithm can be achieved without affecting its time complexity, and experimental results are provided to demonstrate speedups of up to two orders of magnitude for common problem sizes, when compared with the correct baseline algorithm from Deb.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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