RecSplit: Minimal Perfect Hashing via Recursive Splitting
Bibliographic record
Abstract
A minimal perfect hash function bijectively maps a key set S out of a universe U into the first |S| natural numbers. Minimal perfect hash functions are used, for example, to map irregularly-shaped keys, such as strings, in a compact space so that metadata can then be simply stored in an array. While it is known that just 1.44 bits per key are necessary to store a minimal perfect hash function, no published technique can go below 2 bits per key in practice. We propose a new technique for storing minimal perfect hash functions with expected linear construction time and expected constant lookup time that makes it possible to build for the first time, for example, structures which need 1.56 bits per key, that is, within 8.3% of the lower bound, in less than 2 ms per key. We show that instances of our construction are able to simultaneously beat the construction time, space usage and lookup time of the state-of-the-art data structure reaching 2 bits per key. Moreover, we provide parameter choices giving structures which are competitive with alternative, larger-size data structures in terms of space and lookup time. The construction of our data structures can be easily parallelized or mapped on distributed computational units (e.g., within the MapReduce framework), and structures larger than the available RAM can be directly built in mass storage.
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How this classification was reachedexpand
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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".