An index data structure for matrices, with applications to fast two-dimensional pattern matching

Abstract

We describe a new data structure, the submatrix trees (strees for short). It is a forest of compacted patricia trees representing all sub-matrices of a given matrix TEXT. It can be efficiently built and used to answer quickly a wide variety of queries about TEXT. It can be thought of as a generalization to matrices of the suffix tree of a string [14]. We also introduce the notion of an abstract index data structure for matrices, of which the s-trees is an incarnation, and investigate the inherent space and time needed to build it. We show that the s-trees are optimal for space and within a log factor optimal for time.