Abstract
We propose multi-dimensional index data structures that generalize suffix arrays to square matrices and cubic matrices. Giancarlo proposed a two-dimensional index data structure, the Lsuffix tree, that generalizes suffix trees to square matrices. However, the construction algorithm for Lsuffix trees maintains complicated data structures and uses a large amount of space. We present simple and practical construction algorithms for multi-dimensional suffix arrays by applying a new partitioning technique to lexicographic sorting. Our contributions are the following:(1) We present the first algorithm for constructing two-dimensional suffix arrays directly. Our algorithm is ten times faster and five time space-efficient than Giancarlo's algorithm for Lsuffix trees. (2) We present an efficient algorithm for three-dimensional suffix arrays, which is the first algorithm for constructing three-dimensional index data structures.
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