Order-preserving Pattern Research Articles

A fast algorithm for 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. 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.

On the Distribution of the Number of Occurrences of an Order-Preserving Pattern of Length Three in a Random Permutation

Recently, a considerable number of papers in computer science and mathematics examined the number of permutations containing exactly s occurrences of a prescribed order-preserving pattern (or forbidden pattern). It is well known that, mathematically, this is an NP-hard problem. Even in the simple case where the length of an order-preserving pattern is three, the number of permutations of size n containing s (s ≥ 3) order-preserving patterns remains unknown (see Fulmek Adv Appl Math 30(4):607–632, 2003). This manuscript provides a probabilistic approach to enumerate the number of permutations that contain exactly s occurrences of an order-preserving pattern of length three. The method is based on the insertion procedure of the finite Markov chain imbedding technique. Numerical results are provided to illustrate the theoretical results.

Extracting regulatory modules from gene expression data by sequential pattern mining

BackgroundIdentifying a regulatory module (RM), a bi-set of co-regulated genes and co-regulating conditions (or samples), has been an important challenge in functional genomics and bioinformatics. Given a microarray gene-expression matrix, biclustering has been the most common method for extracting RMs. Among biclustering methods, order-preserving biclustering by a sequential pattern mining technique has native advantage over the conventional biclustering approaches since it preserves the order of genes (or conditions) according to the magnitude of the expression value. However, previous sequential pattern mining-based biclustering has several weak points in that they can easily be computationally intractable in the real-size of microarray data and sensitive to inherent noise in the expression value.ResultsIn this paper, we propose a novel sequential pattern mining algorithm that is scalable in the size of microarray data and robust with respect to noise. When applied to the microarray data of yeast, the proposed algorithm successfully found long order-preserving patterns, which are biologically significant but cannot be found in randomly shuffled data. The resulting patterns are well enriched to known annotations and are consistent with known biological knowledge. Furthermore, RMs as well as inter-module relations were inferred from the biologically significant patterns.ConclusionsOur approach for identifying RMs could be valuable for systematically revealing the mechanism of gene regulation at a genome-wide level.