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In the grammar-based compression scheme, a given text string is transformed into a context-free grammar $ G $ such that $ L(G)={ omega } $ and then encoded in an appropriate manner. The compression i...s thus regarded as an optimization ploblem of minimizing the size of $ G $ for a given string $ omega $ of length $ n $. For the APX-hard problem an $ O(log n) $ approximation algorithm with arbitrary string is presented. The previously known best approximation ratio was $ O(sqrt{n/log n}) $[8]show more
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