Structural Analysis of Gapped Motifs of a String

Abstract. We investigate the structure of the set of gapped motifs (repeated patterns with don’t cares) of a given string of symbols. A natural equivalence classification is introduced for the motifs, based on their pattern of occurrences, and another classification for the occurrence patterns, based on the induced motifs. Quadratic–time algorithms are given for finding a maximal representative for an equivalence class while the problems of finding a minimal representative are shown NP–complete. Maximal gapped motifs are shown to be composed of blocks that are maximal non–gapped motifs. These can be found using suffix–tree techniques. This leads to a bound on the number of gapped motifs that have a fixed number of non–gapped blocks.

• Type: Conference
• Year: 2007
• Where: MFCS
• Authors: Esko Ukkonen
• Keywords: Gapped Motifs, Maximal Gapped Motifs, Maximal Non–gapped Motifs, MFCS 2007