Sequence alignment graph of two random sequences I and J of lengths m and n , respectively. The black circles are the initiation vertices of local alignment paths just remaining within the large rectangle of the sequence alignment graph before achieving the score y, i.e., the lower local alignment path has length L
(y) within I; and the upper, length L
(y) within J. The gray shaded area is therefore the (random) alignment rectangle that an optimal local alignment must start within to achieve the score y. Thus, if the black circles lie within the gray rectangle, the alignments achieve the score y within m × n alignment rectangle. If the black circles lie further outside the gray rectangle, the alignments do not achieve the score y within m × n alignment rectangle.