Figure 3

Dynamic Programming for optical map alignment. Optical map aligners, such as the aligner by Valouev [7] and SOMA [9] use dynamic programming to compute the optimal scoring alignment. Let cell (i, j) in the dynamic programming matrix, colored in green, represent the optimal partial alignment of the query map of m fragments through the i ^th restriction site to the reference map of n fragments through the j ^th restriction site such that site i is matched to site j. To allow for unmatched restriction sites in the alignment, the score for cell (i, j) is determined by attempting to extend previously computed alignments in an adjacent δ ² region of the matrix, colored in blue. This allows for up to δ - 1 consecutive unmatched sites in both the query and the reference. The alignment method is then O(δ ² mn).