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.
A full version of this paper is available [17]. These results appeared previously as part of a technical report [16].
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Raskhodnikova, S., Ron, D., Rubinfeld, R., Smith, A. (2007). Sublinear Algorithms for Approximating String Compressibility. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_44
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