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Record W2951052484 · doi:10.48550/arxiv.1405.0189

On Hardness of Jumbled Indexing

2014· preprint· en· W2951052484 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenuearXiv (Cornell University) · 2014
Typepreprint
Languageen
FieldComputer Science
TopicAlgorithms and Data Compression
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsOmegaSearch engine indexingCombinatoricsSubstringPreprocessorMatching (statistics)MathematicsSigmaConstant (computer programming)Pattern matchingComputer scienceAlgorithmData structureStatisticsInformation retrievalPhysicsArtificial intelligence

Abstract

fetched live from OpenAlex

Jumbled indexing is the problem of indexing a text $T$ for queries that ask whether there is a substring of $T$ matching a pattern represented as a Parikh vector, i.e., the vector of frequency counts for each character. Jumbled indexing has garnered a lot of interest in the last four years. There is a naive algorithm that preprocesses all answers in $O(n^2|Σ|)$ time allowing quick queries afterwards, and there is another naive algorithm that requires no preprocessing but has $O(n\log|Σ|)$ query time. Despite a tremendous amount of effort there has been little improvement over these running times. In this paper we provide good reason for this. We show that, under a 3SUM-hardness assumption, jumbled indexing for alphabets of size $ω(1)$ requires $Ω(n^{2-ε})$ preprocessing time or $Ω(n^{1-δ})$ query time for any $ε,δ>0$. In fact, under a stronger 3SUM-hardness assumption, for any constant alphabet size $r\ge 3$ there exist describable fixed constant $ε_r$ and $δ_r$ such that jumbled indexing requires $Ω(n^{2-ε_r})$ preprocessing time or $Ω(n^{1-δ_r})$ query time.

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.

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 categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.875
Threshold uncertainty score0.967

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0020.003
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.063
GPT teacher head0.186
Teacher spread0.123 · 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