Optimal Space and Time for Streaming Pattern Matching

TL;DR

This paper introduces new streaming algorithms for pattern matching problems that optimize space and time complexity in an asymmetric streaming model, surpassing previous bounds and providing provable guarantees.

Contribution

It presents the first algorithms for wildcard pattern matching in the asymmetric streaming model with optimal space and time complexity.

Findings

Improved upper bounds for pattern matching algorithms.

Algorithms outperform unconditional lower bounds on memory.

Optimal space and time algorithms for wildcard pattern matching.

Abstract

In this work, we study longest common substring, pattern matching, and wildcard pattern matching in the asymmetric streaming model. In this streaming model, we have random access to one string and streaming access to the other one. We present streaming algorithms with provable guarantees for these three fundamental problems. In particular, our algorithms for pattern matching improve the upper bound and beat the unconditional lower bounds on the memory of randomized and deterministic streaming algorithms. In addition to this, we present algorithms for wildcard pattern matching in the asymmetric streaming model that have optimal space and time.