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Algorithms for the k-Scaled Order-Preserving Pattern Matching Problem
Kyung Bin Park, Youngho Kim, Joong Cha Na, Jeong Seop Sim
http://doi.org/10.5626/JOK.2022.49.8.585
Two strings of the same length are order-isomorphic if the relative orders of their characters are the same. Given text T of length n and pattern P of length m, the order-preserving pattern matching problem is to find all substrings of T that are order-isomorphic to P. Order-preserving pattern matching can be used to analyze time-series data such as stock indices and melodies. In this paper, we defined the k-scaled order-preserving pattern matching problem and proposed an O(n+mlogm)-time algorithm for the problem. We also proposed a parallel algorithm for the problem, which runs in O(m+k) time using O(n+m) threads.
Parallel Computation of Order-Preserving Periods and Order-Preserving Borders of a Set of Strings
http://doi.org/10.5626/JOK.2019.46.12.1232
Given two strings of the same length over an integer alphabet, those two strings are order-isomorphic when they have the same relative ranks. When strings order-isomorphic to T[1..p](1 ≤ p ≤ n) are periodically repeated in T, a representation of the order relations of T[1..p] is referred to as an order-preserving period of T. When a prefix T[1..q] (1 ≤ q ≤ n) of T is order-isomorphic to a suffix T[n-q+1..n] of T, a representation of the order relations of T[1..q] is called an order-preserving border of T. The lengths of all order-preserving periods (resp. all order-preserving borders) of T can be computed in O(n logn) time using the Z-function. Given a set Ŝ=｛S₁, S₂,..., Sr｝of strings of length n over an integer alphabet, we propose parallel algorithms computing the lengths of all order-preserving periods and all order-preserving borders of Ŝ using O(rn) threads in O(n) time by the Z-function. When compared to each sequential algorithm for Dow Jones Industrial Average, the experimental results show that our parallel algorithm for computing the lengths of all order-preserving periods (resp. all order-preserving borders) of Ŝ runs approximately 3.47 (resp. 3.41) times faster when r =1,000, n =10,000.
An Order-Preserving Pattern Matching Algorithm using Fingerprints of Two q-grams
Gwangmo Yoo, Youngho Kim, Jeong Seop Sim
http://doi.org/10.5626/JOK.2018.45.11.1111
Given a text T of length n and a pattern P of length m, the order-preserving pattern matching problem is to find all substrings in T that have the same relative orders as P. Recently, an O(nm+nqlogq+q!)-time order-preserving pattern matching algorithm was proposed that uses fingerprints of q-grams. In this paper, we propose an order-preserving pattern matching algorithm using the fingerprints of two q-grams to improve execution times. The experimental results for randomly generated T (n = 5,000,000) and P (m = 5,10,15) show that our algorithm runs up to approximately 12% faster than the previous algorithm. Also, for T using Dow Jones Industrial Average (n = 34,658) and P (m = 5,10,15) randomly extracted from T, our algorithm runs up to approximately 10% faster than the previous algorithm.
Parallel Computation of Z-Function for Order-Preserving Pattern Matching and Order-Preserving Multiple Pattern Matching
Youkun Shin, Youngho Kim, Jeong Seop Sim
http://doi.org/10.5626/JOK.2018.45.8.778
Given a text T of length n and a pattern P of length m, the order-preserving pattern matching problem is to find all substrings in T which are order-isomorphic to P. Given a text T of length n and a set of patterns W={P₁, P₂,…, Pb}, the order-preserving multiple pattern matching problem is to find all substrings in T which are order-isomorphic to patterns of W. In this paper, we present two parallel algorithms based on the Z-function. The first algorithm for the order-preserving pattern matching problem runs in O(m) time using O(n+hm) threads and the second algorithm for the order-preserving multiple pattern matching problem runs in O(n+M) time using O(b(n+M)) threads, where h is the number of blocks and M is the length of the longest pattern in W. Experimental results show that our parallel algorithm for the order-preserving pattern matching problem is approximately 71.2 times faster than the sequential algorithm when m=10 and n=1,000,000, and that our parallel algorithm for the order-preserving multiple pattern matching problem is approximately 12.2 times faster than the sequential algorithm when b=1,000, m=10, and n=1,000.
A Hashing-Based Algorithm for Order-Preserving Multiple Pattern Matching
Munseong Kang, Sukhyeun Cho, Jeong Seop Sim
Given a text Tand a pattern P, the order-preserving pattern matching problem is to find all substrings in T which have the same relative orders as P. The order-preserving pattern matching problem has been studied in terms of finding some patterns affected by relative orders, not by their absolute values. Given a text T and a pattern set ℙ, the order-preserving multiple pattern matching problem is to find all substrings in T which have the same relative orders as any pattern in ℙ. In this paper, we present a hashing-based algorithm for the order-preserving multiple pattern matching problem.
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