Dynamic 2D Dictionary Matching in Small Space

TL;DR

This paper introduces the first dynamic 2D dictionary matching algorithm that operates efficiently in small space, allowing pattern insertions and deletions with near-linear time complexity, suitable for uniform rectangular patterns.

Contribution

It presents a novel dynamic 2D dictionary matching algorithm that works in small space and supports efficient updates and queries, a significant advancement over previous static methods.

Findings

Achieves almost linear time complexity for dynamic dictionary matching.

Supports pattern insertion and removal proportional to pattern size.

Operates efficiently on uniform rectangular patterns.

Abstract

The dictionary matching problem preprocesses a set of patterns and finds all occurrences of each of the patterns in a text when it is provided. We focus on the dynamic setting, in which patterns can be inserted to and removed from the dictionary, without reprocessing the entire dictionary. This article presents the first algorithm that performs \emph{dynamic} dictionary matching on two-dimensional data within small space. The time complexity of our algorithm is almost linear. The only slowdown is incurred by querying the compressed self-index that replaces the dictionary. The dictionary is updated in time proportional to the size of the pattern that is being inserted to or removed from the dictionary. Our algorithm is suitable for rectangular patterns that are of uniform size in one dimension.