Result: Longest motifs with a functionally equivalent central block
Department of Computer Science, King's College London, London WC2R 2LS, United Kingdom
Dipartimento di Matematica ed Applicazioni, University di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Inria Rhône-Alpes, Laboratoire de Biométrie et Biologie Evolutive, University Claude Bernard, 69622 Villeurbanne, France
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Further Information
This paper presents a generalization of the notion of longest repeats with a block of k don't care symbols introduced by [8] (for k fixed) to longest motifs composed of three parts: a first and last that parameterize match (that is, match via some symbol renaming, initially unknown), and a functionally equivalent central block. Such three-part motifs are called longest block motifs. Different types of functional equivalence, and thus of matching criteria for the central block are considered, which include as a subcase the one treated in [8] and extend to the case of regular expressions with no Kleene closure or complement operation. We show that a single general algorithmic tool that is a non-trivial extension of the ideas introduced in [8] can handle all the various kinds of longest block motifs defined in this paper. The algorithm complexity is, in all cases, in O(n log n).