Mining Maximal Flexible Patterns in a Sequence

Abstract

We consider the problem of enumerating all maximal flexible patterns in an input sequence database for the class of flexible patterns, where a maximal pattern (also called a closed pattern) is the most specific pattern among the equivalence class of patterns having the same list of occurrences in the input. Since our notion of maximal patterns is based on position occurrences, it is weaker than the traditional notion of maximal patterns based on document occurrences. Based on the framework of reverse search, we present an efficient depth-first search algorithm MaxFlex for enumerating all maximal flexible patterns in a given sequence database without duplicates in $O(||{\mathcal{T}}||\times|\Sigma|)$ time per pattern and $O(||{\mathcal T}||)$ space, where $||{\mathcal T}||$ is the size of the input sequence database $\mathcal T$ and |Σ| is the size of the alphabet on which the sequences are defined. This means that the enumeration problem for maximal flexible patterns is shown to be solvable in polynomial delay and polynomial space.

This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Specially Promoted Research, 17002008, 2007 on “semi-structured data mining”, and 18017015, 2007 on “developing high-speed high-quality algorithms for analyzing huge genome database”.