cient Substring Traversal with Su x Arrays

The substring traversal problem is the problem of enumerating all branching substrings appearing in a given text. Although this problem is easily solvable with the su x tree of McCreight (1976), a space e cient and practically fast solution is important. We devise a simple and e cient algorithm that simulates the traversal of the su x tree for a given text with the su x array of Manber and Meyers (1993) and Gonnet, Baeza-Yates, Snider (1992). The algorithm runs in O(n) time and 5n B bulk I/O with the su x array and an additional structure called the height array, while the naive algorithm using binary search on the su x array requires O(n 2 ) time in the worst case. The space requirement 7N bytes of our algorithm is smaller than 15N bytes of the traversal algorithm with the su x tree. A linear time algorthm for computing the height array from the su x and the height arrays is also presented. Computer experiments on real datasets showed that our traversal algorithm with the su x array is an order of magnitude faster than the naive simulation method and comparable to the traversal algorithm with the su x tree.