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 AhoCorasick like data structure for the online dictionary matching problem. Our solution uses a new succinct representation for multilabeled trees, in which each node has a set of labels from a universe of size lambda. We consider lowest labeled ancestor (LLA) queries on multilabeled 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 multilabeled trees for lambda=omega(1) that support LLA queries in O(log(log(lambda))) time. Using this representation of multilabeled 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.
BibTeX  Entry
@InProceedings{kopelowitz_et_al:LIPIcs:2016:6082,
author = {Tsvi Kopelowitz and Ely Porat and Yaron Rozen},
title = {{Succinct Online Dictionary Matching with Improved WorstCase Guarantees}},
booktitle = {27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
pages = {6:16:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770125},
ISSN = {18688969},
year = {2016},
volume = {54},
editor = {Roberto Grossi and Moshe Lewenstein},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6082},
URN = {urn:nbn:de:0030drops60825},
doi = {10.4230/LIPIcs.CPM.2016.6},
annote = {Keywords: Succinct indexing, dictionary matching, AhoCorasick, labeled trees}
}
Keywords: 

Succinct indexing, dictionary matching, AhoCorasick, labeled trees 
Collection: 

27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016) 
Issue Date: 

2016 
Date of publication: 

27.06.2016 