Near-Optimal Search Time in $$\delta $$-Optimal Space, and Vice Versa

Kociumaka, Tomasz; Navarro, Gonzalo; Olivares, Francisco

doi:10.1007/s00453-023-01186-0

Cited by 5 publications

(1 citation statement)

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“…This measure has several attractive properties: it can be computed in linear time and lower-bounds all previous measures of compressibility, including γ, for every text. While δ is known to be unreachable, the measure δ ′ = δ log n log σ δ log n has all the desired properties: Ω(δ ′ ) is the space needed to represent some text family for each n, σ, and δ; within O(δ ′ ) space it is possible to represent every text T and access any length-λ substring of T in time O(λ + log n) [21], together with more powerful operations [21,20,16].…”

Section: Introductionmentioning

confidence: 99%

Balancing Run-Length Straight-Line Programs

Navarro

Olivares

Urbina

2022

String Processing and Information Retrieval

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We explore an extension to straight-line programs (SLPs) that outperforms, for some text families, the measure δ based on substring complexity, a lower bound for most measures and compressors exploiting repetitiveness (which are crucial in areas like Bioinformatics). The extension, called iterated SLPs (ISLPs), allows rules of the formt , for which we show how to extract any substring of length λ, from the represented text T [1 . . n], in time O(λ + log 2 n log log n). This is the first compressed representation for repetitive texts breaking δ while, at the same time, supporting direct access to arbitrary text symbols in polylogarithmic time. As a byproduct, we extend Ganardi et al.'s technique to balance any SLP (so it has a derivation tree of logarithmic height) to a wide generalization of SLPs, including ISLPs.

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