The Longest Common Factor (LCF) of a set of strings is a well studied problem having a wide range of applications in Bioinformatics: from microarrays to DNA sequences analysis. This problem has been solved by Hui (2000) who uses a famous constant-time solution to the Lowest Common Ancestor (LCA) problem in trees coupled with use of suffix trees. A data structure for the LCA problem, although linear in space and construction time, introduces a multiplicative constant in both space and time that reduces the range of applications in many biological applications. In this article we present a new method for solving the LCF problem using the suffix tree structure with an auxiliary array that take space O(n). Our algorithm works in time O(n log a), where n is the total input size and a is the multiplicative constant introduced by the alphabet. a is the size of the alphabet. We also consider a different version of our algorithm that applies to DAWGs. In this case, we prove that the algorithm works in both time and space proportional to data DAWG's size. © 2008 Springer Science+Business Media, LLC.
CITATION STYLE
Crochemore, M., Gabriele, A., Mignosi, F., & Pesaresi, M. (2008). On the longest common factor problem. In IFIP International Federation for Information Processing (Vol. 273, pp. 143–155). https://doi.org/10.1007/978-0-387-09680-3_10
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