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The motif finding problem can be stated simply as follows.
More details about the complexity of the motif finding problem is given in [ 3].
The motif finding problem can be formulated as an ILP as follows.
The local motif finding problem is posed as an SCFG learning problem.
Existing approaches used to solve the motif finding problem can be classified into two main categories [ 7].
These two conditions together guarantee optimality of the final solution for the original SP-based motif finding problem.
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This strategy works well for the unknown length motif finding problems in this paper.
We apply our LP/DEE approach to several motif finding problems.
In this section, we introduce a number of successively more powerful optimality-preserving dead-end elimination (DEE) techniques for pruning graphs corresponding to motif finding problems.
Although there are several variations of the motif finding algorithms, the problem discussed in this paper is defined as follows: without any previous knowledge of the consensus pattern, discover all the occurences of the motifs and then recover a pattern for which all of these instances are within a given number of mutations (or substitutions).
Our basic LP/DEE approach is to: (1) formulate an instance of motif finding as a graph problem (2) apply the DEE techniques described above in the order of increasing complexity so as to prune the graph (3) use mathematical programming to find a solution to the smaller graph problem and (4) evaluate statistical significance.
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