Sublinear algorithms for approximating string compressibility

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 lem- mas that relate the compressibility of a string with respect to LZ77 to the number of distinct short substrings contained in it (its subword complexity, for small). In addition, we show that approximating the compressibility with respect to LZ77 is related to approximating the support size of a distribution.

Original languageEnglish
Pages (from-to)685-709
Number of pages25
Issue number3
StatePublished - Mar 2013


  • Lempel-Ziv
  • Lossless compression
  • Run-length encoding
  • Sublinear algorithms


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