Space efficient linear time construction of suffix arrays

We present a linear time algorithm to sort all the suffixes of a string over a large alphabet of integers. The sorted order of suffixes of a string is also called suffix array, a data structure introduced by Manber and Myers that has numerous applications in pattern matching, string processing, and computational biology. Though the suffix tree of a string can be constructed in linear time and the sorted order of suffixes derived from it, a direct algorithm for suffix sorting is of great interest due to the space requirements of suffix trees. Our result is one of the first linear time suffix array construction algorithms, which improve upon the previously known O(nlogn) time direct algorithms for suffix sorting. It can also be used to derive a different linear time construction algorithm for suffix trees. Apart from being simple and applicable for alphabets not necessarily of fixed size, this method of constructing suffix trees is more space efficient.