Filtration Algorithms for Approximate Order-Preserving Matching

The exact order-preserving matching problem is to find all the substrings of a text T which have the same length and relative order as a pattern P . Like string maching, order-preserving matching can be generalized by allowing the match to be approximate. In approximate order-preserving matching two strings match if they have the same relative order after removing up to k elements in the same positions in both strings. In this paper we present practical solutions for this problem. The methods are based on filtration, and one of them is the first sublinear solution on average. We show by practical experiments that the new solutions are fast and efficient.