motif discovery problem abstracts the task of discovering short, conserved sites in genomic DNA. Pevzner and Sze recently described a precise combinatorial formulation of motif discovery that motivates the following algorithmic challenge: nd twenty planted occurrences of a motif of length fteen in roughly twelve kilobases of genomic sequence, where each occurrence of the motif differs from its consensus in four randomly chosen positions. Such "subtle" motifs, though statistically highly signi cant, expose a weakness in existing motif- nding algorithms, which typically fail to discover them. Pevzner and Sze introduced new algorithms to solve their (15,4)-motif challenge, but these methods do not scale ef ciently to more dif cult problems in the same family, such as the (14,4)-, (16,5)-, and (18,6)-motif problems. We introduce a novel motif-discovery algorithm, PROJECTION, designed to enhance the performance of existing motif nders using random projections of the input's ...