Permuted Pattern Matching Algorithms on Multi-Track Strings

Abstract

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 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.

Similarity Identification Based on Word Trigrams Using Exact String Matching Algorithms

“…The Horspool Boyer-Moore algorithm is one of the most effective algorithms among these algorithms, especially if the string of patterns is longer [4], [16], [17]. The Horspool algorithm removes the good suffix heuristic of the Boyer-Moore algorithm in the pattern matching process so that only the bad-character heuristic is used to compare characters [4], [14], [17], [18]. The Horspool Boyer-Moore algorithm was introduced by Nigel Horspool in 1980 [17].…”

“…The Horspool algorithm had been used as a search method in the Javanese-Indonesian dictionary, where the algorithm had high accuracy (85.3%) with a short execution time (39.9 ms) [22]. The algorithm was superior to the original Boyer-Moore algorithm for multi-track string matching [18]. Another previous study to identify sensor devices using the Horspool algorithm also showed that the algorithm was efficient, especially if the length of the packet being matched was longer [19].…”

Generalized Dictionary Matching Under Substring Consistent Equivalence Relations

“…By using an AC-automaton, all occurrences of patterns in T can be found only by reading T once, which takes O(n log |Σ|) time. Similarly to the KMP algorithm, the AC algorithm is also extended to perform dictionary matching on some variant of strings [10,11,12,13,14]. In order to perform dictionary matching efficiently, the extended AC algorithms encode the patterns in a dictionary and create an automaton from the encoded patterns instead of the patterns itself.…”

“…Many variants of pattern matching problems are studied for various applications such as parameterized pattern matching [6] for detecting duplication in source code, order-preserving pattern matching [14,16] for numerical analysis, permuted pattern matching [13] for multi sensor data, and so on [18]. In order to solve these problems efficiently, the KMP algorithm is extended for the above mentioned pattern matching problems [3,9,11,14,16,18]. Recently, Matsuoka et al [17] defined a general pattern matching problem under a substring consistent equivalence relation.…”

Computing Covers under Substring Consistent Equivalence Relations

“…Equivalence relation Border SCover LCover Identity equivalence O(n) [15] O(n) [8] O(n) [17] Parameterized equivalence O(n log |Π|) [2] O(n log |Π|) O(n log |Π|) Order-isomorphism O(n log n) [14,16] O(n log n) O(n log n) Permuted equivalence O(nk) [11,12] O(nk) O(nk)…”