Sublinear algorithms for approximating string compressibility

Sofya Raskhodnikova; Dana Ron; Ronitt Rubinfeld; Adam Smith

doi:10.1007/978-3-540-74208-1_44

Sublinear algorithms for approximating string compressibility

Sofya Raskhodnikova^*, Dana Ron, Ronitt Rubinfeld, Adam Smith

^*Corresponding author for this work

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

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 Lempel-Ziv (LZ), 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 LZ 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 Lempel-Ziv to the number of distinct short substrings contained in it. In addition, we show that approximating the compressibility with respect to LZ is related to approximating the support size of a distribution.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Publisher	Springer Verlag
Pages	609-623
Number of pages	15
ISBN (Print)	9783540742074
DOIs	https://doi.org/10.1007/978-3-540-74208-1_44
State	Published - 2007
Event	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States Duration: 20 Aug 2007 → 22 Aug 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4627 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
Country/Territory	United States
City	Princeton, NJ
Period	20/08/07 → 22/08/07

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10.1007/978-3-540-74208-1_44

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Raskhodnikova, S., Ron, D., Rubinfeld, R., & Smith, A. (2007). Sublinear algorithms for approximating string compressibility. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings (pp. 609-623). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_44

Raskhodnikova, Sofya ; Ron, Dana ; Rubinfeld, Ronitt et al. / Sublinear algorithms for approximating string compressibility. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. pp. 609-623 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 Lempel-Ziv (LZ), 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 LZ 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 Lempel-Ziv to the number of distinct short substrings contained in it. In addition, we show that approximating the compressibility with respect to LZ is related to approximating the support size of a distribution.",

author = "Sofya Raskhodnikova and Dana Ron and Ronitt Rubinfeld and Adam Smith",

year = "2007",

doi = "10.1007/978-3-540-74208-1_44",

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Raskhodnikova, S, Ron, D , Rubinfeld, R & Smith, A 2007, Sublinear algorithms for approximating string compressibility. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, Springer Verlag, pp. 609-623, 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007, Princeton, NJ, United States, 20/08/07. https://doi.org/10.1007/978-3-540-74208-1_44

Sublinear algorithms for approximating string compressibility. / Raskhodnikova, Sofya; Ron, Dana ; Rubinfeld, Ronitt et al.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. p. 609-623 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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 Lempel-Ziv (LZ), 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 LZ 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 Lempel-Ziv to the number of distinct short substrings contained in it. In addition, we show that approximating the compressibility with respect to LZ is related to approximating the support size of a distribution.

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Raskhodnikova S, Ron D , Rubinfeld R, Smith A. Sublinear algorithms for approximating string compressibility. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag. 2007. p. 609-623. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74208-1_44

Sublinear algorithms for approximating string compressibility

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