Sublinear Algorithms for Approximating String Compressibility
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Rubinfeld_Sublinear algorithms.pdf
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Author(s)
Raskhodnikova, Sofya
Ron, Dana
Rubinfeld, Ronitt
Smith, Adam
Date Issued
February 2012
Journal
Algorithmica
Publisher
Springer-Verlag
Citation
Raskhodnikova, Sofya et al. “Sublinear Algorithms for Approximating String Compressibility.” Algorithmica (2012).
Version
Author's final manuscript
Abstract
We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and a variant of Lempel-Ziv (LZ77), and present sublinear algorithms for approximating compressibility with respect to both schemes. We also give several lower bounds that show that our algorithms for both schemes cannot be improved significantly.
Our investigation of LZ77 yields results whose interest goes beyond the initial questions we set out to study. In particular, we prove combinatorial structural lemmas that relate the compressibility of a string with respect to LZ77 to the number of distinct short substrings contained in it (its ℓth subword complexity , for small ℓ). In addition, we show that approximating the compressibility with respect to LZ77 is related to approximating the support size of a distribution.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00453-012-9618-6
