Suffix trees and suffix arrays

The Burrows-Wheeler Transform has a very close relationship with suffix trees and suffix arrays — the array of indexes to the sorted array of substrings generated during the transform is essentially a suffix array, which in turn is a representation of the information in a suffix tree. As pointed out by Burrows and Wheeler in their original work (Burrows and Wheeler, 1994), the problem of sorting the rotated matrices is the major bottleneck in performing the transformation, and this is essentially an exercise in suffix sorting. This relationship between the BWT and suffix arrays and suffix trees also has important implications in the applications of the BWT, and in its relationship with other compression schemes, such as PPM. Analyzing the performance of the BWT is greatly simplified by an understanding of the construction and complexity of suffix trees and suffix arrays.

In this chapter we study suffix trees and suffix arrays in more detail. While this is motivated by their relationship with the BWT, suffix trees and suffix arrays have become important data structures in their own right, especially for problems in pattern matching, full-text indexing, compression, and other applications.