A Space-Saving Approximation Algorithm for Grammar-Based Compression
Hiroshi Sakamoto, Shirou Maruyama, Takuya Kida, Shinichi Shimozono · IEICE Transactions on Information and Systems · 2009
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 • • • 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].