Biomedical Engineering Reference
In-Depth Information
In this new equation,
MaxValue
is some function of variables
A
i
,
B
j
, and
C
k
, where
i
,
j
, and
k
are
indices to the variables defined in the tree structure illustrated in
Figure 8-9
. The best solution to
MaxValue
is in the form [
i
= 3,
j
= 3,
k
= 2], for example. As in the simpler 2D problem, a matrix of
solutions can be constructed. However, the matrix of solutions is now much larger, and is better
represented as a 3D structure, as in
Figure 8-10
.
Figure 8-10. Solution Matrix for
MaxValue
=
f
(
A
i
,
B
j
,
C
k
). Only one value for
k
(
k
= 0) is shown here for clarity.
Even though there are now many more solutions to consider, the process of evaluating
MaxValue
for
three variables and saving intermediary results in the 3D matrix is the same as in the previous 2D
example. Adding additional dimensions, although computationally intensive, makes it possible to
evaluate all possible ways of aligning the three sequences against each other in a reasonable time,
