The Smallest Grammar Problem Revisited

被引：5

作者：

Bannai, Hideo ^{[1
]}

Hirayama, Momoko ^{[2
]}

Hucke, Danny ^{[3
]}

Inenaga, Shunsuke ^{[2
]}

Jez, Artur ^{[4
]}

Lohrey, Markus ^{[3
]}

Reh, Carl Philipp ^{[3
]}

机构：

[1] Tokyo Med & Dent Univ, Dept Data Sci Algorithm Design & Anal, Tokyo 1138510, Japan

[2] Kyushu Univ, Dept Informat, Fukuoka 8190395, Japan

[3] Univ Siegen, Dept Elect Engn & Comp Sci, D-57076 Siegen, Germany

[4] Univ Wroclaw, Inst Comp Sci, PL-50383 Wroclaw, Poland

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 01期

关键词：

String compression; smallest grammar problem; approximation algorithm; LZ78; RePair; COMPRESSED STRINGS; APPROXIMATION; SEQUENCES;

D O I：

10.1109/TIT.2020.3038147

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 a gap between the lower and upper bound. Here the gaps for LZ78 and BISECTION are closed by showing that the approximation ratio of LZ78 is Theta((n/log n)(2/3)), whereas the approximation ratio of BISECTION is Theta(n/log n). In addition, the lower bound for RePair is improved from Omega(root log n) to Omega(log n/ log log n). Finally, results of Arpe and Reischuk relating grammar-based compression for arbitrary alphabets and binary alphabets are improved.

引用

页码：317 / 328

页数：12

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