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URN: urn:nbn:de:0030-drops-16937
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1693/
Sakamoto, Hiroshi

A Space-Saving Approximation Algorithm for Grammar-Based Compression

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Abstract

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].

BibTeX - Entry

@InProceedings{sakamoto:DSP:2008:1693,
  author =	{Hiroshi Sakamoto},
  title =	{A Space-Saving Approximation Algorithm for Grammar-Based Compression},
  booktitle =	{Structure-Based Compression of Complex Massive Data },
  year =	{2008},
  editor =	{Stefan B{\"o}ttcher and Markus Lohrey and Sebastian Maneth and Wojcieh Rytter},
  number =	{08261},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1693},
  annote =	{Keywords: Grammar based compression, space efficient approximation}
}

Keywords: Grammar based compression, space efficient approximation
Seminar: 08261 - Structure-Based Compression of Complex Massive Data
Issue date: 2008
Date of publication: 20.11.2008

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