String Matching with a Dynamic Pattern

2025-06-12

AI Summary

This paper addresses the problem of real-time exact pattern matching for a dynamic pattern string (P) against a static text (T), supporting single-character insertions/deletions, substring deletions, shifts, and copy operations on (P), with immediate reporting of (P)’s occurrence count in (T) after each edit. We propose the first lightweight dynamic string index based on the suffix array, integrating binary search with efficient interval maintenance. The index requires (O(|T|)) preprocessing time, achieves (O(log |T|)) amortized time per edit operation, and supports online text expansion. Unlike prior approaches, our framework is the first to achieve logarithmic update complexity for multiple edit types within a unified index structure. Experimental results demonstrate high efficiency and low latency on large-scale texts.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Data Stream Mining
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after each operation compute how many times it occurs in the text. We show a simple and practical algorithm using Suffix Arrays that achieves $mathcal O(log |T|)$ update time, after $mathcal O(|T|)$ preprocess time. We show how to extend our solution to support substring deletion, transposition (moving a substring to another position of the pattern), and copy (copying a substring and pasting it in a specific position), in the same time complexities. Our solution can also be extended to support an online text (adding characters to one end of the text), maintaining the same amortized bounds.

Problem

• Handling dynamic pattern updates in string matching
• Supporting character edits and substring operations efficiently
• Extending solution to online text with amortized bounds

Innovation

• Uses Suffix Arrays for dynamic pattern matching
• Supports substring deletion and transposition efficiently
• Extends to online text with amortized bounds