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

共 50 条

[1] The Smallest Grammar Problem Revisited
Hucke, Danny
Lohrey, Markus
Reh, Carl Philipp
STRING PROCESSING AND INFORMATION RETRIEVAL, SPIRE 2016, 2016, 9954 : 35 - 49
[2] The smallest grammar problem
Charikar, M
Lehman, E
Liu, D
Panigrahy, R
Prabhakaran, M
Sahai, A
Shelat, A
IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (07) : 2554 - 2576
[3] An Effective Heuristic for the Smallest Grammar Problem
Benz, Florian
Koetzing, Timo
GECCO'13: PROCEEDINGS OF THE 2013 GENETIC AND EVOLUTIONARY COMPUTATION CONFERENCE, 2013, : 487 - 494
[4] The Smallest Grammar Problem as Constituents Choice and Minimal Grammar Parsing
Carrascosa, Rafael
Coste, Francois
Galle, Matthias
Infante-Lopez, Gabriel
ALGORITHMS, 2011, 4 (04) : 262 - 284
[5] Choosing Word Occurrences for the Smallest Grammar Problem
Carrascosa, Rafael
Coste, Francois
Galle, Matthias
Infante-Lopez, Gabriel
LANGUAGE AND AUTOMATA THEORY AND APPLICATIONS, 2010, 6031 : 154 - +
[6] On the Complexity of the Smallest Grammar Problem over Fixed Alphabets
Casel, Katrin
Fernau, Henning
Gaspers, Serge
Gras, Benjamin
Schmid, Markus L.
THEORY OF COMPUTING SYSTEMS, 2021, 65 (02) : 344 - 409
[7] On the Complexity of the Smallest Grammar Problem over Fixed Alphabets
Katrin Casel
Henning Fernau
Serge Gaspers
Benjamin Gras
Markus L. Schmid
Theory of Computing Systems, 2021, 65 : 344 - 409
[8] A really simple approximation of smallest grammar
Jez, Artur
THEORETICAL COMPUTER SCIENCE, 2016, 616 : 141 - 150
[9] Approximation of smallest linear tree grammar
Jez, Artur
Lohrey, Markus
INFORMATION AND COMPUTATION, 2016, 251 : 215 - 251
[10] Approximation of smallest linear tree grammar
Jez, Artur
Lohrey, Markus
31ST INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2014), 2014, 25 : 445 - 457

← 1 2 3 4 5 →