The Smallest Grammar Problem Revisited
نویسندگان
چکیده
In a seminal paper, Charikar et al. derive upper and lower bounds on the approximation ratios for several grammar-based compressors, but in all cases there is gap between bound. Here gaps LZ78 BISECTION are closed by showing that ratio of ?((n/log n) 2/3 ), whereas ?(?(n/log n)). addition, bound RePair improved from ?(?(log n)) to ?(log n/log log n). Finally, results Arpe Reischuk relating compression arbitrary alphabets binary improved.
منابع مشابه
The Smallest Grammar Problem Revisited
In a seminal paper of Charikar et al. on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors, but in all cases there is a gap between the lower and upper bound. Here we close the gaps for LZ78 and BISECTION by showing that the approximation ratio of LZ78 is Θ((n/ logn)), whereas the approximation ratio of BISE...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2021
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2020.3038147