License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.122
URN: urn:nbn:de:0030-drops-62570
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6257/
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Casel, Katrin ; Fernau, Henning ; Gaspers, Serge ; Gras, Benjamin ; Schmid, Markus L.

On the Complexity of Grammar-Based Compression over Fixed Alphabets

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LIPIcs-ICALP-2016-122.pdf (0.6 MB)

Abstract

It is shown that the shortest-grammar problem remains NP-complete if the alphabet is fixed and has a size of at least 24 (which settles an open question). On the other hand, this problem can be solved in polynomial-time, if the number of nonterminals is bounded, which is shown by encoding the problem as a problem on graphs with interval structure. Furthermore, we present an O(3n) exact exponential-time algorithm, based on dynamic programming. Similar results are also given for 1-level grammars, i.e., grammars for which only the start rule contains nonterminals on the right side (thus, investigating the impact of the "hierarchical depth" on the complexity of the shortest-grammar problem).

BibTeX - Entry

@InProceedings{casel_et_al:LIPIcs:2016:6257,
  author =	{Katrin Casel and Henning Fernau and Serge Gaspers and Benjamin Gras and Markus L. Schmid},
  title =	{{On the Complexity of Grammar-Based Compression over Fixed Alphabets}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{122:1--122:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6257},
  URN =		{urn:nbn:de:0030-drops-62570},
  doi =		{10.4230/LIPIcs.ICALP.2016.122},
  annote =	{Keywords: Grammar-Based Compression, Straight-Line Programs, NP-Completeness, Exact Exponential Time Algorithms}
}

Keywords: Grammar-Based Compression, Straight-Line Programs, NP-Completeness, Exact Exponential Time Algorithms
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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