Finding the longest common nonsuperstring in linear time

Abstract

String inclusion and non-inclusion problems have been vigorously studied in such diverse fields as molecular biology, data compression, and computer security. Among the well-known string inclusion or non-inclusion notions, we are interested in the longest common nonsuperstring. Given a set of strings, the longest common nonsuperstring problem is finding the longest string that is not a superstring of any string in the given set. It is known that the longest common nonsuperstring problem is solvable in polynomial time. In this paper, we propose an efficient algorithm for the longest common nonsuperstring problem. The running time of our algorithm is linear with respect to the sum of the lengths of the strings in the given set, using generalized suffix trees.