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Open AccessArticle

Permuted Pattern Matching Algorithms on Multi-Track Strings

Graduate School of Information Sciences, Tohoku University, Miyagi 980-8579, Japan
Author to whom correspondence should be addressed.
Algorithms 2019, 12(4), 73;
Received: 28 February 2019 / Revised: 2 April 2019 / Accepted: 3 April 2019 / Published: 8 April 2019
(This article belongs to the Special Issue String Matching and Its Applications)
A multi-track string is a tuple of strings of the same length. Given the pattern and text of two multi-track strings, the permuted pattern matching problem is to find the occurrence positions of all permutations of the pattern in the text. In this paper, we propose several algorithms for permuted pattern matching. Our first algorithm, which is based on the Knuth–Morris–Pratt (KMP) algorithm, has a fast theoretical computing time with O ( m k ) as the preprocessing time and O ( n k log σ ) as the matching time, where n, m, k, σ , and occ denote the length of the text, the length of the pattern, the number of strings in the multi-track, the alphabet size, and the number of occurrences of the pattern, respectively. We then improve the KMP-based algorithm by using an automaton, which has a better experimental running time. The next proposed algorithms are based on the Boyer–Moore algorithm and the Horspool algorithm that try to perform pattern matching. These algorithms are the fastest experimental algorithms. Furthermore, we propose an extension of the AC-automaton algorithm that can solve dictionary matching on multi-tracks, which is a task to find multiple multi-track patterns in a multi-track text. Finally, we propose filtering algorithms that can perform permuted pattern matching quickly in practice. View Full-Text
Keywords: multi-track string; permuted pattern matching; AC-automaton multi-track string; permuted pattern matching; AC-automaton
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Hendrian, D.; Ueki, Y.; Narisawa, K.; Yoshinaka, R.; Shinohara, A. Permuted Pattern Matching Algorithms on Multi-Track Strings. Algorithms 2019, 12, 73.

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