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.SWAT.2016.10
URN: urn:nbn:de:0030-drops-60256
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6025/
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Ganguly, Arnab ; Hon, Wing-Kai ; Shah, Rahul

A Framework for Dynamic Parameterized Dictionary Matching

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LIPIcs-SWAT-2016-10.pdf (0.5 MB)

Abstract

Two equal-length strings S and S' are a parameterized-match (p-match) iff there exists a one-to-one function that renames the characters in S to those in S'. Let P be a collection of d patterns of total length n characters that are chosen from an alphabet Sigma of cardinality sigma. The task is to index P such that we can support the following operations.

* search(T): given a text T, report all occurrences <j,P_i> such that there exists a pattern P_i in P that is a p-match with the substring T[j,j+|P_i|-1].

* ins(P_i)/del(P_i): modify the index when a pattern P_i is inserted/deleted.

We present a linear-space index that occupies O(n*log n) bits and supports (i) search(T) in worst-case O(|T|*log^2 n + occ) time, where occ is the number of occurrences reported, and (ii) ins(P_i) and del(P_i) in amortized O(|P_i|*polylog(n)) time.
Then, we present a succinct index that occupies (1+o(1))n*log sigma + O(d*log n) bits and supports (i) search(T) in worst-case O(|T|*log^2 n + occ) time, and (ii) ins(P_i) and del(P_i) in amortized O(|P_i|*polylog(n)) time. We also present results related to the semi-dynamic variant of the problem, where deletion is not allowed.

BibTeX - Entry

@InProceedings{ganguly_et_al:LIPIcs:2016:6025,
  author =	{Arnab Ganguly and Wing-Kai Hon and Rahul Shah},
  title =	{{A Framework for Dynamic Parameterized Dictionary Matching}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6025},
  URN =		{urn:nbn:de:0030-drops-60256},
  doi =		{10.4230/LIPIcs.SWAT.2016.10},
  annote =	{Keywords: Parameterized Dictionary Indexing, Generalized Suffix Tree, Succinct Data Structures, Sparsification}
}

Keywords: Parameterized Dictionary Indexing, Generalized Suffix Tree, Succinct Data Structures, Sparsification
Collection: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 22.06.2016

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