2026-07-22T20:50:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:10484 2024-03-06T10:45:51Z ddc:004 open_access

Compressed Multiple Pattern Matching Kosolobov, Dmitry Sivukhin, Nikita multiple pattern matching compressed space Aho--Corasick automaton 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 kth-order 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 worst-case 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dmitry Kosolobov and Nikita Sivukhin 2019 Is Part Of LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2019.13 urn:nbn:de:0030-drops-104847 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.13 eng https://creativecommons.org/licenses/by/3.0/legalcode