Improving on-line construction of two-dimensional suffix trees for square matrices

Abstract

The two-dimensional (2-D) suffix tree of an n x n square matrix A is a compacted trie that represents all square submatrices of A. We consider constructing 2-D suffix trees on-line, which means, instead of giving the whole matrix A in advance, A is separated and each part of A is given at different time as algorithms proceed. In general, developing an on-line algorithm is more difficult than developing an off-line algorithm. Moreover, the smaller the input grain size is, the harder it is to develop an on-line algorithm. In the case of 2-D suffix tree construction, dealing with a character at a time is harder than dealing with a row or a column at a time. In this paper we propose a randomized linear-time algorithm for constructing 2-D suffix trees on-line. This algorithm is superior to previous algorithms in two ways: (1) This is the first linear-time algorithm for constructing 2-D suffix trees on-line. Although there have been some linear-time algorithms for off-line construction, there were no linear-time algorithms for on-line construction. (2) We deal with the most fine-grain on-line case, i.e., our algorithm can construct a 2-D suffix tree even though only one character of A is given at a time, while previous on-line algorithms require at least a row and/or a column at a time.