The longest common substring problem

Given a set (Formula presented.) of q documents, the Longest Common Substring (LCS) problem asks, for any integer 2 ? k ? q, the longest substring that appears in k documents. LCS is a well-studied problem having a wide range of applications in Bioinformatics: from microarrays to DNA sequences alignments and analysis. This problem has been solved by Hui (2000 International Journal of Computer Science and Engineering 15 73-76) by using a famous constant-time solution to the Lowest Common Ancestor (LCA) problem in trees coupled with the use of suffix trees. In this article, we present a simple method for solving the LCS problem by using suffix trees (STs) and classical union-find data structures. In turn, we show how this simple algorithm can be adapted in order to work with other space efficient data structures such as the enhanced suffix arrays (ESA) and the compressed suffix tree.