Sequence Comparison.pdf

3.6 Space-Saving Strategies 49
Fig. 3.14 There are seven ways entering the three grid points of an entry (i, j).
{
D ′ D
(i, j)=max
′ (i − 1, j),
S(i − 1, j) − α − l × β;
{ I(i, j − 1) − β,
I(i, j)=max
S(i, j − 1) − α − β;
{
I ′ I
(i, j)=max
′ (i, j − 1),
S(i, j − 1) − α − l × β;
⎧
D(i, j),
⎪⎨ D ′ (i, j),
S(i, j)=max I(i, j),
I ⎪⎩
′ (i, j),
S(i − 1, j − 1)+σ(a i ,b j ).
3.6 Space-Saving Strategies
Straightforward implementation of the dynamic-programming algorithms utilizes
quadratic space to produce an optimal global or local alignment. For analysis of
long DNA sequences, this space restriction is more crucial than the time constraint.