Abstract: Generalized Center String (GCS) problem are
generalized from Common Approximate Substring problem
and Common substring problems. GCS are known to be
NP-hard allowing the problems lies in the explosion of
potential candidates. Finding longest center string without
concerning the sequence that may not contain any motifs is
not known in advance in any particular biological gene
process. GCS solved by frequent pattern-mining techniques
and known to be fixed parameter tractable based on the
fixed input sequence length and symbol set size. Efficient
method known as Bpriori algorithms can solve GCS with
reasonable time/space complexities. Bpriori 2 and Bpriori
3-2 algorithm are been proposed of any length and any
positions of all their instances in input sequences. In this
paper, we reduced the time/space complexity of Bpriori
algorithm by Constrained Based Frequent Pattern mining
(CBFP) technique which integrates the idea of Constraint
Based Mining and FP-tree mining. CBFP mining technique
solves the GCS problem works for all center string of any
length, but also for the positions of all their mutated copies
of input sequence. CBFP mining technique construct TRIE
like with FP tree to represent the mutated copies of center
string of any length, along with constraints to restraint
growth of the consensus tree. The complexity analysis for
Constrained Based FP mining technique and Bpriori
algorithm is done based on the worst case and average case
approach. Algorithm's correctness compared with the
Bpriori algorithm using artificial data is shown.