[Paper Review] Efficient Algorithms for the Order Preserving Pattern Matching Problem

Simone Faro, Oğuzhan Külekci|arXiv (Cornell University)|Jan 16, 2015

Algorithms and Data Compression8 references4 citations

TL;DR

This paper presents two novel filtering-based algorithms for the order-preserving pattern matching (OPPM) problem, transforming input sequences into larger-alphabet representations to accelerate search and drastically reduce false positives. Experimental results show the proposed methods are up to 2× faster than prior approaches, reducing false positives by up to 99% under optimal conditions.

ABSTRACT

Given a pattern x of length m and a text y of length n, both over an ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. It is an approximate variant of the well known exact pattern matching problem which has gained attention in recent years. This interesting problem finds applications in a lot of fields as time series analysis, like share prices on stock markets, weather data analysis or to musical melody matching. In this paper we present two new filtering approaches which turn out to be much more effective in practice than the previously presented methods. From our experimental results it turns out that our proposed solutions are up to 2 times faster than the previous solutions reducing the number of false positives up to 99%

Motivation & Objective

• Address the need for faster and more accurate solutions to the order-preserving pattern matching (OPPM) problem, which arises in time series analysis and music data processing.
• Overcome limitations of existing OPPM algorithms that suffer from high false positive rates and suboptimal filtering efficiency.
• Develop new filtering techniques that operate on larger alphabets to improve search performance and reduce spurious matches.
• Evaluate the proposed methods against state-of-the-art algorithms across diverse synthetic and periodic sequences.
• Demonstrate practical superiority in both speed and precision under real-world applicable conditions.

Proposed method

• Propose two new families of filtering approaches that map original sequences into sequences over larger alphabets to enhance filtering power.
• Design filters that preserve relative order while enabling faster comparison via optimized data structures and preprocessing.
• Introduce a novel filtering mechanism (Nr) that achieves high efficiency by reducing candidate matches early in the process.
• Implement a second filtering strategy (No) that further reduces false positives at the cost of slightly higher preprocessing overhead.
• Use a two-phase approach: first apply the filtering step to eliminate non-candidates, then perform exact order-isomorphism checks only on remaining candidates.
• Leverage the structure of periodic sequences to evaluate robustness and scalability across varying pattern lengths and alphabet characteristics.

Experimental results

Research questions

• RQ1 Can filtering techniques operating on larger alphabets significantly outperform existing OPPM algorithms in terms of speed and false positive reduction?
• RQ2 How do the proposed filtering methods scale with increasing pattern length and varying sequence periodicity?
• RQ3 What is the trade-off between preprocessing cost and runtime performance in the new filtering frameworks?
• RQ4 To what extent can the new methods reduce false positives while maintaining or improving search efficiency?
• RQ5 How do the proposed algorithms compare to Chhabra and Tarhio’s binary-based filtering method in practice?

Key findings

• The proposed Nr filtering approach achieves up to a 1.7× speedup over previous methods, especially effective for long patterns on periodic sequences.
• The No filtering approach reduces false positives by up to 99.8%, demonstrating superior precision, particularly on longer patterns.
• The Nr4 variant achieves a false positive reduction of nearly 100% in some configurations, outperforming all prior methods.
• On periodic sequences with period 5, the Nr1 method achieves a 1.3× speedup, while the Fct algorithm remains competitive for short patterns.
• The new methods reduce the number of false positives by up to 99% under suitable conditions, significantly improving filtering accuracy.
• Overall, the proposed algorithms are up to 2× faster than existing solutions, with consistent performance gains across diverse test sequences.