Parameterized Matching in the Streaming Model

TL;DR

This paper presents a streaming algorithm for parameterized pattern matching that operates in constant time per symbol and uses near optimal sublinear space, surpassing previous limitations for pattern matching problems.

Contribution

It introduces the first sublinear, near optimal space solution for parameterized matching in streaming models, extending the scope beyond exact matching.

Findings

Constant time per symbol processing

Sublinear, near optimal space complexity

Achieves solutions for more complex matching problems

Abstract

We study the problem of parameterized matching in a stream where we want to output matches between a pattern of length m and the last m symbols of the stream before the next symbol arrives. Parameterized matching is a natural generalisation of exact matching where an arbitrary one-to-one relabelling of pattern symbols is allowed. We show how this problem can be solved in constant time per arriving stream symbol and sublinear, near optimal space with high probability. Our results are surprising and important: it has been shown that almost no streaming pattern matching problems can be solved (not even randomised) in less than Theta(m) space, with exact matching as the only known problem to have a sublinear, near optimal space solution. Here we demonstrate that a similar sublinear, near optimal space solution is achievable for an even more challenging problem. The proof is considerably more complex than that for exact matching.