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1. Approximation Ratios of on Unary Strings

Author

Hucke, Danny, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Brisaboa, Nieves R., editor, and Puglisi, Simon J., editor

Published
2019
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2. The Smallest Grammar Problem Revisited

Author

Hucke, Danny, Lohrey, Markus, Reh, Carl Philipp, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Inenaga, Shunsuke, editor, Sadakane, Kunihiko, editor, and Sakai, Tetsuya, editor

Published
2016
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3. Approximation Ratios of RePair, LongestMatch and Greedy on Unary Strings †.

Author

Hucke, Danny, Reh, Carl Philipp, and Miritescu, Catalina-Ana

Subjects
*GREEDY algorithms, *APPROXIMATION algorithms, *DATA compression
Abstract

A grammar-based compressor is an algorithm that receives a word and outputs a context-free grammar that only produces this word. The approximation ratio for a single input word is the size of the grammar produced for this word divided by the size of a smallest grammar for this word. The worst-case approximation ratio of a grammar-based compressor for a given word length is the largest approximation ratio over all input words of that length. In this work, we study the worst-case approximation ratio of the algorithms Greedy, RePair and LongestMatch on unary strings, i.e., strings that only make use of a single symbol. Our main contribution is to show the improved upper bound of O ((log n) 8 · (log log n) 3) for the worst-case approximation ratio of Greedy. In addition, we also show the lower bound of 1.34847194 ⋯ for the worst-case approximation ratio of Greedy, and that RePair and LongestMatch have a worst-case approximation ratio of log 2 (3) . [ABSTRACT FROM AUTHOR]

Published
2021
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