An exact data mining method for finding center strings and all their instances

Common substring problems allowing errors are known to be NP-hard. The main challenge of the problems lies in the combinatorial explosion of potential candidates. In this paper, we propose and study a Generalized Center String (GCS) problem, where not only all models (center strings) of any length, but also the positions of all their (degenerative) instances in input sequences are searched for. Inspired by frequent pattern mining techniques in data mining field, we present an exact and efficient method to solve GCS. First, a highly parallelized TRIE-like structure, consensus tree, is proposed. Based on this structure, we present three Bpriori algorithms step by step. Bpriori algorithms can solve GCS with reasonable time and/or space complexities. We have proved that GCS is fixed parameter tractable with respect to fixed symbol set size and fixed length of input sequences. Experiment results on both artificial and real data have shown the correctness of the algorithms and the validity of our complexity analysis. A comparison with some current algorithms for solving Common Approximate Substring problems is also given.