Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Nishimoto, Takaaki; I, Tomohiro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki http://www.dagstuhl.de/lipics License
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Fully Dynamic Data Structure for LCE Queries in Compressed Space

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Abstract

A Longest Common Extension (LCE) query on a text T of length N asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding G of size w = O(min(z log N log^* M, N)) [Mehlhorn et al., Algorithmica 17(2):183-198, 1997] of T, which can be seen as a compressed representation of T, has a capability to support LCE queries in O(log N + log ell log^* M) time, where ell is the answer to the query, z is the size of the Lempel-Ziv77 (LZ77) factorization of T, and M >= 4N is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, G can be enhanced to support efficient update operations: After processing G in O(w f_A) time, we can insert/delete any (sub)string of length y into/from an arbitrary position of T in O((y + log Nlog^* M) f_A) time, where f_A = O(min{ (loglog M loglog w)/(logloglog M), sqrt(log w/loglog w)}). This yields the first fully dynamic LCE data structure working in compressed space. We also present efficient construction algorithms from various types of inputs: We can construct G in O(N f_A) time from uncompressed string T; in O(n loglog (n log^* M) log N log^* M) time from grammar-compressed string T represented by a straight-line program of size n; and in O(z f_A log N log^* M) time from LZ77-compressed string T with z factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.

BibTeX - Entry

@InProceedings{nishimoto_et_al:LIPIcs:2016:6504,
  author =	{Takaaki Nishimoto and Tomohiro I and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda},
  title =	{{Fully Dynamic Data Structure for LCE Queries in Compressed Space}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{72:1--72:15},
  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/2016/6504},
  URN =		{urn:nbn:de:0030-drops-65045},
  doi =		{10.4230/LIPIcs.MFCS.2016.72},
  annote =	{Keywords: dynamic texts,  longest common extension (LCE) queries, straight-line program}
}

Keywords: dynamic texts, longest common extension (LCE) queries, straight-line program
Seminar: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue date: 2016
Date of publication: 2016


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