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On the longest common factor problem

Abstract : 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 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.
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Submitted on : Thursday, February 14, 2013 - 8:37:37 AM
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  • HAL Id : hal-00620280, version 1


Maxime Crochemore, Alessandra Gabriele, Filippo Mignosi, Mauriana Pesaresi. On the longest common factor problem. 5th IFIP International Conference on Theoretical Computer Science (TCS'08), Sep 2008, United States. pp.143-155. ⟨hal-00620280⟩



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