Order-preserving pattern matching with k mismatches

TL;DR

This paper introduces an efficient algorithm for order-preserving pattern matching that allows up to k mismatches, improving search flexibility while maintaining computational efficiency for small k values.

Contribution

It presents the first algorithm for order-preserving pattern matching with mismatches, achieving near-linear time complexity for small k.

Findings

Algorithm detects order-preserving matches with mismatches in O(n(loglogm + kloglogk)) time.

Efficiently handles small k values, making it practical for real-world applications.

Advances the field by combining order-preserving matching with mismatch tolerance.

Abstract

We study a generalization of the recently introduced order-preserving pattern matching, where instead of looking for an exact copy of the pattern, we only require that the relative order between the elements is the same. In our variant, we additionally allow up to k mismatches between the pattern and the text, and the goal is to construct an efficient algorithm for small values of k. For a pattern of length m and a text of length n, our algorithm detects an order-preserving occurrence with up to k mismatches in O(n(loglogm + kloglogk)) time.