Full-fledged Real-Time Indexing for Constant Size Alphabets

TL;DR

This paper introduces a real-time indexing data structure for pattern matching over constant-size alphabets, enabling efficient updates and queries in dynamically arriving texts, solving a long-standing open problem.

Contribution

It presents a novel data structure supporting constant-time symbol prepends and efficient pattern matching queries in real-time for constant-size alphabets.

Findings

Supports pattern matching in O(|P|+k) time

Allows prepending symbols in O(1) worst-case time

Resolves a long-standing open problem in real-time string indexing

Abstract

In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet ofconstant size. Each new symbol can be prepended to $T$ in O(1) worst-case time. At any moment, we can report all occurrences of a pattern $P$ in the current text in $O(|P|+k)$ time, where $|P|$ is the length of $P$ and $k$ is the number of occurrences. This resolves, under assumption of constant-size alphabet, a long-standing open problem of existence of a real-time indexing method for string matching (see \cite{AmirN08}).