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A Note on Random Suffix Search Trees

2002· book-chapter· en· W73714569 on OpenAlexaff
Luc Devroye, Ralph Neininger

Bibliographic record

VenueBirkhäuser Basel eBooks · 2002
Typebook-chapter
Languageen
FieldComputer Science
TopicAlgorithms and Data Compression
Canadian institutionsMcGill University
Fundersnot available
KeywordsCombinatoricsSuffix treeMathematicsIndependent and identically distributed random variablesRandom binary treeSelf-balancing binary search treeTree (set theory)Binary search treeSuffixOptimal binary search treeSequence (biology)Binary treeBinary numberBinary logarithmSearch treeDiscrete mathematicsK-ary treeRandom variableSearch algorithmAlgorithmTree structureArithmeticStatisticsChemistry

Abstract

fetched live from OpenAlex

A random suffix search tree is a binary search> tree constructed for the suffixes Xi = 0.BiBi+1Bi+2... of a sequence B1, B2... of independent identically distributed random b- ary digits Bj. Let Dn denote the depth of the node for Xn in this tree when B1 is uniform on ℤb. We show that for any value of $$b > 1, \mathbb{E}{{\text{D}}_n} = 2 \log n + O({\log ^2}\log n)$$ just as for the random binary search tree. We also show that $${D_n}/\mathbb{E}{{\text{D}}_n} \to 1$$ in probability.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.902
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0020.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.002

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.

Opus teacher head0.037
GPT teacher head0.251
Teacher spread0.215 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

Study designNot applicable
Domainnot available
GenreOther

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".

Quick stats

Citations0
Published2002
Admission routes1
Has abstractyes

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