Crochemore's Repetitions Algorithm Revisited - Computing Runs.
Bibliographic record
Abstract
Crochemore's repetitions algorithm introduced in 1981 was the first O(n log n) algorithm for computing repetitions. Since then, several linear-time worst-case algorithms for computing runs have been introduced. They all follow a similar strategy: first compute the suffix tree or array, then use the suffix tree or array to compute the Lempel-Ziv factorization, then using the Lempel-Ziv factorization compute all the runs. It is conceivable that in practice an extension of Crochemore's repetitions algorithm may outperform the linear-time algorithms, or at least for certain classes of strings. The nature of Crochemore's algorithm lends itself naturally to parallelization, while the linear-time algorithms are not easily conducive to parallelization. For all these reasons it is interesting to explore ways to extend the original Crochemore's repetitions algorithm to compute runs. We present three variants of extending the repetitions algorithm to compute runs: two with a worsen complexity of O(n (log n)2), and one with the same complexity as the original algorithm. The three variants are tested for speed of performance and their memory requirements are analyzed. The third variant is tested and analyzed for various memory-saving alterations. The purpose of this research is to identify the best extension of Crochemore's algorithm for further study, comparison with other algorithms, and parallel implementation.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.004 |
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".