Abstract
Given d strings over the alphabet {0,1,...,sigma{}1}, the classical Aho  Corasick data structure allows us to find all occ occurrences of the strings in any text T in O(T + occ) time using O(m log m) bits of space, where m is the number of edges in the trie containing the strings. Fix any constant epsilon in (0, 2). We describe a compressed solution for the problem that, provided sigma <=m^delta for a constant delta < 1, works in O(T 1/epsilon log(1/epsilon) + occ) time, which is O(T + occ) since epsilon is constant, and occupies mH_k + 1.443 m + epsilon m + O(d log m/d) bits of space, for all 0 <= k <= max{0,alpha log_sigma m  2} simultaneously, where alpha in (0,1) is an arbitrary constant and H_k is the kthorder empirical entropy of the trie. Hence, we reduce the 3.443m term in the space bounds of previously best succinct solutions to (1.443 + epsilon)m, thus solving an open problem posed by Belazzougui. Further, we notice that L = log binom{sigma (m+1)}{m}  O(log(sigma m)) is a worstcase space lower bound for any solution of the problem and, for d = o(m) and constant epsilon, our approach allows to achieve L + epsilon m bits of space, which gives an evidence that, for d = o(m), the space of our data structure is theoretically optimal up to the epsilon m additive term and it is hardly possible to eliminate the term 1.443m. In addition, we refine the space analysis of previous works by proposing a more appropriate definition for H_k. We also simplify the construction for practice adapting the fixed block compression boosting technique, then implement our data structure, and conduct a number of experiments showing that it is comparable to the state of the art in terms of time and is superior in space.
BibTeX  Entry
@InProceedings{kosolobov_et_al:LIPIcs:2019:10484,
author = {Dmitry Kosolobov and Nikita Sivukhin},
title = {{Compressed Multiple Pattern Matching}},
booktitle = {30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
pages = {13:113:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771030},
ISSN = {18688969},
year = {2019},
volume = {128},
editor = {Nadia Pisanti and Solon P. Pissis},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10484},
URN = {urn:nbn:de:0030drops104847},
doi = {10.4230/LIPIcs.CPM.2019.13},
annote = {Keywords: multiple pattern matching, compressed space, AhoCorasick automaton}
}
Keywords: 

multiple pattern matching, compressed space, AhoCorasick automaton 
Collection: 

30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) 
Issue Date: 

2019 
Date of publication: 

06.06.2019 