https://hal.archives-ouvertes.fr/hal-00620280Crochemore, MaximeMaximeCrochemoreLIGM - Laboratoire d'Informatique Gaspard-Monge - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École des Ponts ParisTech - ESIEE Paris - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche ScientifiqueGabriele, AlessandraAlessandraGabrieleDipartimento di Matematica e Applicazioni [Palermo] - Università degli studi di Palermo - University of PalermoMignosi, FilippoFilippoMignosiDI - Dipartimento di Informatica [Italy] - UNIVAQ - Università degli Studi dell'AquilaPesaresi, MaurianaMaurianaPesaresiDI - Dipartimento di Informatica [Pisa] - University of Pisa - Università di Pisa On the longest common factor problemHAL CCSD2008[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Crochemore, MaximeAusiello G. and Karhumäki J. and Mauri G. and Ong C.-H. L.2013-02-14 08:37:372022-09-29 14:21:152013-02-14 11:39:32enConference papersapplication/pdf1The 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.