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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2015.302
URN: urn:nbn:de:0030-drops-49220
URL: http://drops.dagstuhl.de/opus/volltexte/2015/4922/
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Fernau, Henning ; Manea, Florin ; Mercas, Robert ; Schmid, Markus L.

Pattern Matching with Variables: Fast Algorithms and New Hardness Results

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Abstract

A pattern (i. e., a string of variables and terminals) maps to a word, if this is obtained by uniformly replacing the variables by terminal words; deciding this is NP-complete. We present efficient algorithms\footnote{The computational model we use is the standard unit-cost RAM with logarithmic word size. Also, all logarithms appearing in our time complexity evaluations are in base 2.} that solve this problem for restricted classes of patterns. Furthermore, we show that it is NP-complete to decide, for a given number k and a word w, whether w can be factorised into k distinct factors; this shows that the injective version (i.e., different variables are replaced by different words) of the above matching problem is NP-complete even for very restricted cases.

BibTeX - Entry

@InProceedings{fernau_et_al:LIPIcs:2015:4922,
  author =	{Henning Fernau and Florin Manea and Robert Mercas and Markus L. Schmid},
  title =	{{Pattern Matching with Variables: Fast Algorithms and New Hardness Results}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{302--315},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4922},
  URN =		{urn:nbn:de:0030-drops-49220},
  doi =		{10.4230/LIPIcs.STACS.2015.302},
  annote =	{Keywords: combinatorial pattern matching, combinatorics on words, patterns with variables, ${cal NP}$-complete string problems}
}

Keywords: combinatorial pattern matching, combinatorics on words, patterns with variables, ${cal NP}$-complete string problems
Seminar: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 25.02.2015


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