Order Preserving Matching

TL;DR

This paper introduces efficient algorithms for order-preserving matching in numeric strings, enabling pattern matching based on relative order relations, with applications in stock analysis and music matching.

Contribution

It defines new representations of order relations and develops optimized algorithms for single and multiple pattern order-preserving matching problems.

Findings

Single pattern matching achieved in O(n + m log m) time.

Multiple pattern matching achieved in O(n log m) time.

Algorithms are applicable to real-world scenarios like stock and melody analysis.

Abstract

We introduce a new string matching problem called order-preserving matching on numeric strings where a pattern matches a text if the text contains a substring whose relative orders coincide with those of the pattern. Order-preserving matching is applicable to many scenarios such as stock price analysis and musical melody matching in which the order relations should be matched instead of the strings themselves. Solving order-preserving matching has to do with representations of order relations of a numeric string. We define prefix representation and nearest neighbor representation, which lead to efficient algorithms for order-preserving matching. We present efficient algorithms for single and multiple pattern cases. For the single pattern case, we give an O(n log m) time algorithm and optimize it further to obtain O(n + m log m) time. For the multiple pattern case, we give an O(n log m) time algorithm.