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Computing DAWGs and Minimal Absent Words in Linear Time for Integer Alphabets

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Abstract

The directed acyclic word graph (DAWG) of a string y is the smallest (partial) DFA which recognizes all suffixes of y and has only O(n) nodes and edges. We present the first O(n)-time algorithm for computing the DAWG of a given string y of length n over an integer alphabet of polynomial size in n. We also show that a straightforward modification to our DAWG construction algorithm leads to the first O(n)-time algorithm for constructing the affix tree of a given string y over an integer alphabet. Affix trees are a text indexing structure supporting bidirectional pattern searches. As an application to our O(n)-time DAWG construction algorithm, we show that the set MAW(y) of all minimal absent words of y can be computed in optimal O(n + |MAW(y)|) time and O(n) working space for integer alphabets.

BibTeX - Entry

@InProceedings{fujishige_et_al:LIPIcs:2016:6452,
  author =	{Yuta Fujishige and Yuki Tsujimaru and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda},
  title =	{{Computing DAWGs and Minimal Absent Words in Linear Time for Integer Alphabets}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6452},
  URN =		{urn:nbn:de:0030-drops-64528},
  doi =		{10.4230/LIPIcs.MFCS.2016.38},
  annote =	{Keywords: string algorithms, DAWGs, suffix trees, minimal absent words}
}

Keywords: string algorithms, DAWGs, suffix trees, minimal absent words
Seminar: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue date: 2016
Date of publication: 2016


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