Sublinear algorithms for approximating string compressibility

Sofya Raskhodnikova, Dana Ron, Ronitt Rubinfeld, Adam Davison Smith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Pages609-623
Number of pages15
StatePublished - Dec 1 2007
Event10th 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: Aug 20 2007Aug 22 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4627 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
CountryUnited States
CityPrinceton, NJ
Period8/20/078/22/07

Fingerprint

Compressibility
Strings
Run-length Encoding
Lossless Compression
Lemma
Compression
Lower bound
Distinct

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Raskhodnikova, S., Ron, D., Rubinfeld, R., & Smith, A. D. (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).
Raskhodnikova, Sofya ; Ron, Dana ; Rubinfeld, Ronitt ; Smith, Adam Davison. / 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. 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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Raskhodnikova, S, Ron, D, Rubinfeld, R & Smith, AD 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, 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, 8/20/07.

Sublinear algorithms for approximating string compressibility. / Raskhodnikova, Sofya; Ron, Dana; Rubinfeld, Ronitt; Smith, Adam Davison.

Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. 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 proceedingConference contribution

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Raskhodnikova S, Ron D, Rubinfeld R, Smith AD. 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. 2007. p. 609-623. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).