Bit-parallel (δ, γ)-matching and suffix automata

Maxime Crochemore, Costas Iliopoulos, Gonzalo Navarro, Yoan Pinzon, Alejandro Salinger

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

(δ,γ)-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P1…m and a text T1…n on an alphabet of integers, find the occurrences P′ of the pattern in the text such that (i) View the MathML source, and (ii) View the MathML source. The problem makes sense for δ⩽γ⩽δm. Several techniques for (δ,γ)-matching have been proposed, based on bit-parallelism or on skipping characters. We first present an O(mnlog(γ)/w) worst-case time and O(n) average-case time bit-parallel algorithm (being w the number of bits in the computer word). It improves the previous O(mnlog(δm)/w) worst-case time algorithm of the same type. Second, we combine our bit-parallel algorithm with suffix automata to obtain the first algorithm that skips characters using both δ and γ. This algorithm examines less characters than any previous approach, as the others do just δ-matching and check the γ-condition on the candidates. We implemented our algorithms and drew experimental results on real music, showing that our algorithms are superior to current alternatives with high values of δ.
Original languageEnglish
Pages (from-to)198 - 214
Number of pages17
JournalJournal of Discrete Algorithms
Volume3
Issue number2-4
DOIs
Publication statusPublished - Jun 2005

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