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Succinct Online Dictionary Matching with Improved Worst-Case Guarantees

Authors: Tsvi Kopelowitz, Ely Porat, and Yaron Rozen

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)


Abstract
In the online dictionary matching problem the goal is to preprocess a set of patterns D={P_1,...,P_d} over alphabet Sigma, so that given an online text (one character at a time) we report all of the occurrences of patterns that are a suffix of the current text before the following character arrives. We introduce a succinct Aho-Corasick like data structure for the online dictionary matching problem. Our solution uses a new succinct representation for multi-labeled trees, in which each node has a set of labels from a universe of size lambda. We consider lowest labeled ancestor (LLA) queries on multi-labeled trees, where given a node and a label we return the lowest proper ancestor of the node that has the queried label. In this paper we introduce a succinct representation of multi-labeled trees for lambda=omega(1) that support LLA queries in O(log(log(lambda))) time. Using this representation of multi-labeled trees, we introduce a succinct data structure for the online dictionary matching problem when sigma=omega(1). In this solution the worst case cost per character is O(log(log(sigma)) + occ) time, where occ is the size of the current output. Moreover, the amortized cost per character is O(1+occ) time.

Cite as

Tsvi Kopelowitz, Ely Porat, and Yaron Rozen. Succinct Online Dictionary Matching with Improved Worst-Case Guarantees. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{kopelowitz_et_al:LIPIcs.CPM.2016.6,
  author =	{Kopelowitz, Tsvi and Porat, Ely and Rozen, Yaron},
  title =	{{Succinct Online Dictionary Matching with Improved Worst-Case Guarantees}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.6},
  URN =		{urn:nbn:de:0030-drops-60825},
  doi =		{10.4230/LIPIcs.CPM.2016.6},
  annote =	{Keywords: Succinct indexing, dictionary matching, Aho-Corasick, labeled trees}
}
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