Indexed Two-Dimensional String Matching

O(n 2 log n) Time On-Line Construction of Two-Dimensional Suffix Trees

The two-dimensional suffix tree of an n × n square matrix A is a compacted trie that represents all square submatrices of Ai¾?[9]. For the off-line case, i.e., A is given in advance to the algorithm, it is known how to build it in optimal time, for any type of alphabet sizei¾?[9,15]. Motivated by applications in Image Compressioni¾?[18], Giancarlo and Guaianai¾?[12] considered the on-line version of the two-dimensional suffix tree and presented an On2log2n-time algorithm, which we refer to as GG. That algorithm is a non-trivial generalization of Ukkonen's on-line algorithm for standard suffix trees [19]. The main contribution in this paper is an Olog n factor improvement in the time complex…

$O(n^2 log n)$ Time On-line Construction of Two-Dimensional Suffix Trees

The two-dimensional suffix tree of an n × n square matrix A is a compacted trie that represents all square submatrices of A [11]. For the off-line case, i.e., A is given in advance to the algorithm, it is known how to build it in optimal time, for any type of alphabet size [11], [18]. Motivated by applications in Image Compression [22], Giancarlo and Guaiana [14] considered the on-line version of the two-dimensional suffix tree and presented an O(n2 log2 n)-time algorithm, which we refer to as GG. That algorithm is a nontrivial generalization of Ukkonen’s on-line algorithm for standard suffix trees [23]. The main contribution in this paper is an O(logn) factor improvement in the time comple…