Generalizations of suffix arrays to multi-dimensional matrices

We propose multi-dimensional index data structures that generalize su x arrays to square matrices and cubic matrices. Giancarlo proposed a two-dimensional index data structure, the Lsu x tree, that generalizes su x trees to square matrices. However, the construction algorithm for Lsu x trees maintains complicated data structures and uses a large amount of space. We present simple and practical construction algorithms for multi-dimensional su x arrays by applying a new partitioning technique to lexicographic sorting. Our contributions are the following: (1) We present the rst algorithm for constructing two-dimensional su x arrays directly. Our algorithm is ten times faster and ve times space-e cient than Giancarlo's algorithm for Lsu x trees. (2) We present an e cient algorithm for three-dimensional su x arrays, which is the rst algorithm for constructing three-dimensional index data structures. Contact Author: Kunsoo Park. E-mail: [email protected]. School of Computer Sci. and Eng., Seoul National University, Seoul 151-742, Korea. Supported by Pusan National University Research Grant. Supported by S.N.U. Research Fund 99-11-1-063 and the Brain Korea 21 Project.