An Improved Order-Preserving Pattern Matching Algorithm Using Fingerprints

• Published in: Mathematics (Basel) Vol. 10; no. 12; p. 1954
• Main Authors: Kim, Youngjoon, Kim, Youngho, Sim, Jeong Seop
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.06.2022
• Subjects: Algorithms; bad character heuristic; Fingerprints; Heuristic; Isomorphism; Mathematics; Number systems; order isomorphism; order-preserving pattern matching; Pattern matching; Time series
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10121954

Two strings of the same length are order isomorphic if their relative orders are the same. The order-preserving pattern matching problem is to find all substrings of text T that are order isomorphic to pattern P when T(|T|=n) and P(|P|=m) are given. An O(mn+nqlogq+q!)-time algorithm using the O(m+q!) space for the order-preserving pattern matching problem has been proposed utilizing fingerprints of q-grams based on the factorial number system and the bad character heuristic. In this paper, we propose an O(mn+2q)-time algorithm using the O(m+2q) space for the order-preserving pattern matching problem, but utilizing fingerprints of q-grams converted to binary numbers. A comparative experiment using three types of time series data demonstrates that the proposed algorithm is faster than existing algorithms because it reduces the number of order isomorphism tests.