Near-real-time Solutions for Online String Problems

2026-02-16

AI Summary

This work presents the first online algorithms achieving worst-case poly-log-logarithmic time per character for several classical problems in online string processing, including maintaining the longest repeated suffix array, (reverse) LZ77 factorization, and minimal unique substrings. Building upon the Breslauer–Italiano online suffix tree construction and leveraging irreducible representations of string data structures, the proposed approach operates within linear space while significantly improving upon prior methods that only offered amortized bounds or higher logarithmic complexities. Furthermore, the study establishes an efficient transformation between the longest previous factor array and the longest repeated suffix array, enabling sublinear-sized updates to these arrays.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings, including the computation of the longest repeating suffix array, the (reversed) Lempel-Ziv 77 factorization, and the maintenance of minimal unique substrings, all in an online manner. Our solutions improve over the best known running times for these problems in terms of the worst-case time per letter, for which we achieve a poly-log-logarithmic time complexity, within a linear space. Best known results for these problems require a poly-logarithmic time complexity per letter or only provide amortized complexity bounds. As a result of independent interest, we give conversions between the longest previous factor array and the longest repeating suffix array in space and time bounds based on their irreducible representations, which can have sizes sublinear in the length of the input string.

Problem

• online string problems
• near-real-time
• worst-case time complexity
• suffix tree
• Lempel-Ziv factorization

Innovation

• online suffix tree
• poly-log-logarithmic time
• longest repeating suffix array
• Lempel-Ziv 77 factorization
• minimal unique substrings