Linear-Time Sequence Comparison Using Minimal Absent Words & Applications
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as q-gram distance, are usually computed in time linear with respect to the length of the sequences. In this article, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an absent word of some sequence if it does not occur in the sequence. An absent word is minimal if all its proper factors occur in the sequence. Here we present the first linear-time and linear-space algorithm to compare two sequences by considering all their minimal absent words. In the process, we present results of combinatorial interest, and also extend the proposed techniques to compare circular sequences.
KeywordsAlgorithms on strings Sequence comparison Alignment-free comparison Absent words Forbidden words Circular words
We warmly thank Alice Heliou for her inestimable code contribution and Antonio Restivo for useful discussions. Gabriele Fici’s work was supported by the PRIN 2010/2011 project “Automi e Linguaggi Formali: Aspetti Matematici e Applicativi” of the Italian Ministry of Education (MIUR) and by the “National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA – INdAM). Robert Mercaş’s work was supported by the P.R.I.M.E. programme of DAAD co-funded by BMBF and EU’s 7th Framework Programme (grant 605728). Solon P. Pissis’s work was supported by a Research Grant (#RG130720) awarded by the Royal Society.
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