Multiple choice tries and distributed hash tables
Bibliographic record
Abstract
Abstract In this article we consider tries built fromnstrings such that each string can be chosen from a pool ofkstrings, each of them generated by a discrete i.i.d. source. Three cases are considered:k= 2,kis large but fixed, andk˜clogn. The goal in each case is to obtain tries as balanced as possible. Various parameters such as height and fill‐up level are analyzed. It is shown that for two‐choice tries a 50% reduction in height is achieved when compared with ordinary tries. In a greedy online construction when the string that minimizes the depth of insertion for every pair is inserted, the height is only reduced by 25%. To further reduce the height by another 25%, we design a more refined online algorithm. The total computation time of the algorithm isO(nlogn). Furthermore, when we choose the best amongk≥ 2 strings, then for large but fixedkthe height is asymptotically equal to the typical depth in a trie. Finally, we show that further improvement can be achieved if the number of choices for each string is proportional to logn. In this case highly balanced trees can be constructed by a simple greedy algorithm for which the difference between the height and the fill‐up level is bounded by a constant with high probability. This, in turn, has implications for distributed hash tables, leading to a randomized ID management algorithm in peer‐to‐peer networks such that, with high probability, the ratio between the maximum and the minimum load of a processor is O(1). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".