Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms

2026-04-21

AI Summary

This work addresses the challenge of string processing—such as pattern matching and compression—in asymmetric streaming models, where algorithms are constrained to sublinear space and a single pass over the input. The authors propose a suffix random-access data structure that reframes the problem within an online read-only model to efficiently leverage a reference string. Their key contributions include establishing a two-way reduction between suffix random access and the cryptographic function inversion problem, and designing locally sparse string synchronizing sets that enable streaming construction. Building on this framework, they develop state-of-the-art streaming algorithms for exact and approximate (Hamming and edit distance) pattern matching as well as relative Lempel-Ziv compression, significantly outperforming existing approaches in performance.

Technology Category

• Data Mining & Knowledge Management: Data Stream Mining
• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Security and Privacy: Applications of cryptography

Abstract

Many string processing problems can be phrased in the streaming setting, where the input arrives symbol by symbol and we have sublinear working space. The area of streaming algorithms for string processing has flourished since the seminal work of Porat and Porat [FOCS 2009]. Unfortunately, problems with efficient solutions in the classical setting often do not admit efficient solutions in the streaming setting. As a bridge between these two settings, Saks and Seshadhri [SODA 2013] introduced the asymmetric streaming model. Here, one is given read-only access to a (typically short) reference string $R$ of length $m$, while a text $T$ arrives as a stream. We provide a generic technique to reduce fundamental string problems in the asymmetric streaming model to the online read-only model, lifting several existing algorithms and generally improving upon the state of the art. Most notably, we obtain asymmetric streaming algorithms for exact and approximate pattern matching (under both the Hamming and edit distances), and for relative Lempel-Ziv compression. At the heart of our approach lies a novel tool that facilitates efficient computation in the asymmetric streaming model: the suffix random access data structure. In its simplest variant, it maintains constant-time random access to the longest suffix of (the seen prefix of) $T$ that occurs in $R$. We show a bidirectional reduction between suffix random access and function inversion, a central problem in cryptography. On the way to our upper bound, we propose a variant of the string synchronizing sets ([Kempa and Kociumaka; STOC 2019]) with a local sparsity condition that, as we show, admits an efficient streaming construction algorithm. We believe that our framework and techniques will find broad applications in the development of small-space string algorithms.

Problem

• asymmetric streaming
• string algorithms
• suffix random access
• function inversion
• streaming model

Innovation

• suffix random access
• function inversion
• asymmetric streaming
• string synchronizing sets
• streaming algorithms