A Space-Saving Approximation Algorithm for Grammar-Based Compression

Author Hiroshi Sakamoto

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Hiroshi Sakamoto

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Hiroshi Sakamoto. A Space-Saving Approximation Algorithm for Grammar-Based Compression. In Structure-Based Compression of Complex Massive Data. Dagstuhl Seminar Proceedings, Volume 8261, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


A space-efficient approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. For the input length n and an optimum CFG size g, the algorithm consumes only O(g log g) space and O(n log^n) time to achieve O((log^n) log n) approximation ratio to the optimum compression, where log^n is the maximum number of logarithms satisfying log log · · · logn > 1. This ratio is thus regarded to almost O(log n), which is the currently best approximation ratio. While g depends on the string, it is known that g =(log n) and g=O(n/log_k n) for strings from a k-letter alphabet [12].
  • Grammar based compression
  • space efficient approximation


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