A Space-Saving Approximation Algorithm for Grammar-Based Compression

Hiroshi SAKAMOTO, Shirou MARUYAMA, Takuya KIDA, Shinichi SHIMOZONO
2009 IEICE transactions on information and systems  
Hiroshi SAKAMOTO †a) , Member, Shirou MARUYAMA † †b) , Takuya KIDA † † †c) , and Shinichi SHIMOZONO †d) , Nonmembers SUMMARY 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
more » ... compression, where log * n is the maximum number of logarithms satisfying log log · · · log n > 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 = Ω(log n) and g = O n log k n for strings from k-letter alphabet [12] .
doi:10.1587/transinf.e92.d.158 fatcat:aj43d6v2zvb2pbganpte7dpfzi