Dual-pivot and beyond: The potential of multiway partitioning in quicksort
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Since 2011 the Java runtime library uses a Quicksort variant with two pivot elements. For reasons that remained unclear for years it is faster than the previous Quicksort implementation by more than 10 %; this is not only surprising because the previous code was highly-tuned and is used in many programming libraries, but also since earlier theoretical investigations suggested that using several pivots in Quicksort is not helpful. In my dissertation I proved by a comprehensive mathematical analysis of all sensible Quicksort partitioning variants that (a) indeed there is hardly any advantage to be gained from multiway partitioning in terms of the number of comparisons (and more generally in terms of CPU costs), but (b) multiway partitioning does significantly reduce the amount of data to be moved between CPU and main memory. Moreover, this more efficient use of the memory hierarchy is not achieved by any of the other well-known optimizations of Quicksort, but only through the use of several pivots.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| 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