On-line construction of two-dimensional suffix trees

Abstract

We say that a data structure is builton-lineif, at any instant, we have the data structure corresponding to the input we have seen up to that instant. For instance, consider the suffix tree of a stringx[1,n]. An algorithm building iton-lineis such that, when we have read the firstisymbols ofx[1,n], we have the suffix tree forx[1,i]. We present a new technique, which we refer to asimplicit updates, based on which we obtain: (a) an algorithm for theon-lineconstruction of the Lsuffix tree of ann×nmatrixA - this data structure is the two-dimensional analog of the suffix tree of a string; (b) simple algorithms implementing primitive operations forLZ1-typeon-line losslessimage compression methods. Those methods, recently introduced by Storer, are generalizations ofLZ1-typecompression methods for strings. For the problem in (a), we get nearly an order of magnitude improvement over algorithms that can be derived from known techniques. For the problem in (b), we do not get an asymptotic speed-up with respect to what can be done with known techniques; rather we show that our algorithms are a natural support for the primitive operations. This may lead to faster implementations of those primitive operations. To the best of our knowledge, our technique is the first one that effectively addresses problems related to theon-lineconstruction of two-dimensional suffix trees. © 1999 Academic Press.