Computing Longest Common Substrings Via Suffix Arrays

Given a set of N strings A = {α1, . . . , αN} of total length n over alphabet Σ one may ask to find, for a fixed integer K, 2 ≤ K ≤ N , the longest substring β that appears in at least K strings in A. It is known that this problem can be solved in O(n) time with the help of suffix trees. However, the resulting algorithm is rather complicated. Also, its running time and memory consumption may depend on |Σ|. This paper presents an alternative, remarkably simple approach to the above problem, which relies on the notion of suffix arrays. Once the suffix array of some auxiliary O(n)-length string is computed, one needs a simple O(n)-time postprocessing to find the requested longest substring. Since a number of efficient and simple linear-time algorithms for constructing suffix arrays has been recently developed (with constant not depending on |Σ|), our approach seems to be quite practical.