Sukhyeun Cho

A fast algorithm for order-preserving pattern matching

We present a new method of deciding the order-isomorphism between two strings.We show that the bad character rule can be applied to the OPPM problem.We present a space-efficient algorithm computing the shift table for text search.We present a linear-time algorithm for an integer alphabet in the worst case. Given a text T and a pattern P, the order-preserving pattern matching (OPPM) problem is to find all substrings in T which have the same relative orders as P. The OPPM has been studied in the fields of finding some patterns affected by relative orders, not by their absolute values. In this paper, we present a method of deciding the order-isomorphism between two strings even when there are same characters. Then, we show that the bad character rule of the Horspool algorithm for generic pattern matching problems can be applied to the OPPM problem and we present a space-efficient algorithm for computing shift tables for text search. Finally, we combine our bad character rule with the KMP-based algorithm to improve the worst-case running time. We give experimental results to show that our algorithm is about 2 to 6 times faster than the KMP-based algorithm in reasonable cases.

Fast Order-Preserving Pattern Matching

Given a text T and a pattern P, the order-preserving pattern matching (OPPM) problem is to find all substrings in T which have the same relative orders as P. The OPPM has been studied in the fields of finding some patterns affected by relative orders, not by their absolute values. For example, it can be applied to time series analysis like share prices on stock markets and to musical melody matching of two musical scores. In this paper, we present a new method of deciding the order-isomorphism between two strings even when there are same characters. Then, we show that the bad character rule of the Horspool algorithm for generic pattern matching problems can be applied to the OPPM problem. Finally, we present a fast algorithm for the OPPM problem and give experimental results to show that our algorithm is about 2 to 5 times faster than the KMP-based algorithm in reasonable cases.

Improved Algorithms for the Boxed-Mesh Permutation Pattern Matching Problem

Recently, various types of permutation patterns such as mesh patterns, boxed-mesh patterns, and consecutive patterns, have been studied where relative order between characters is considered rather than characters themselves. Among these, we focus on boxed-mesh patterns and study the problem of finding all boxed-subsequences of a text \(T\) of length \(n\) whose relative order between characters is the same as that of a pattern \(P\) of length \(m\). Recently, it is known that this problem can be solved in \(O(n^3)\) time. In this paper, we first propose an \(O(n^2 m)\)-time algorithm for the problem based on interesting properties of boxed subsequences. Then, we give a further improved algorithm which runs in \(O(n^2 \log m)\) time using preprocessed information on \(P\) and order-statistics trees.

An O(n2logm)-time algorithm for the boxed-mesh permutation pattern matching problem

Abstract Given a text T of length n and a pattern P of length m over a numeric alphabet Σ, the boxed-mesh permutation pattern matching problem is to find all boxed-subsequences of T whose relative order between all characters is the same as that of P. In this paper, we propose an O ( n 2 log ⁡ m ) -time algorithm for the boxed-mesh permutation pattern matching problem based on interesting properties of boxed subsequences, using preprocessed information on P and order-statistic trees.

Fast Multiple Order-Preserving Matching Algorithms

Given a text T and a pattern P, the order-preserving matching problem is to find all substrings in T which have the same relative orders as P. Order-preserving matching has been an active research area since it was introduced by Kubica et al. [13] and Kim et al. [11]. In this paper we present two algorithms for the multiple order-preserving matching problem, one of which runs in sublinear time on average and the other in linear time on average. Both algorithms run much faster than the previous algorithms.

A new graph model and algorithms for consistent superstring problems.

Problems related to string inclusion and non-inclusion have been vigorously studied in diverse fields such as data compression, molecular biology and computer security. Given a finite set of positive strings and a finite set of negative strings , a string α is a consistent superstring if every positive string is a substring of α and no negative string is a substring of α. The shortest (resp. longest) consistent superstring problem is to find a string α that is the shortest (resp. longest) among all the consistent superstrings for the given sets of strings. In this paper, we first propose a new graph model for consistent superstrings for given and . In our graph model, the set of strings represented by paths satisfying some conditions is the same as the set of consistent superstrings for and . We also present algorithms for the shortest and the longest consistent superstring problems. Our algorithms solve the consistent superstring problems for all cases, including cases that are not considered in previous work. Moreover, our algorithms solve in polynomial time the consistent superstring problems for more cases than the previous algorithms. For the polynomially solvable cases, our algorithms are more efficient than the previous ones.