Discovery of functionally significant short, statistically overrepresented subsequence patterns (motifs) in a set of sequences is a challenging problem in bioinformatics. Oftentimes, not all sequences in the set contain a motif. These non-motif-containing sequences complicate the algorithmic discovery of motifs. Filtering the non-motif-containing sequences from the larger set of sequences while simultaneously determining the identity of the motif is, therefore, desirable and a non-trivial problem in motif discovery research.