Dynamic 2D Dictionary Matching in Small Space

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.