bove alignment has three matches in addition to four mismatches,

first residue of sequence x (which is C) is aligned with the first

f sequence y (which is C as well), the second residue of sequence

is C) is aligned with the second residue of sequence y (which is

) and the fourth residue of sequence x (which is A) is aligned with

h residue of sequence y (which is A as well),

other alignment between these two sequences may show a

alignment format as shown below, where there are four matches

mismatches,

G

T

be seen that there will be many possible alignments for any two

s. Each of these alignments will have a different alignment

s well as an alignment statistic such as the number of matches as

he number of mismatches plus the number of the inserted gaps.

the number of matches and the number of mismatches as well as

ber of inserted gaps are incorporated into a unique alignment

Among all possible alignments, if they can be exhausted, there

one (or more than one) homology alignment which has the

d alignment statistic. Therefore, a sequence homology alignment

s an optimisation process. It is a process of discovering the best

y alignment with an optimised alignment statistic.

oubt, an exhaustive search is impossible if sequences are

ntly long. Therefore the best approach is to employ a heuristic

ion process. One of the best approaches for this kind of

ion process is the dynamic programming algorithm [Kirk, 1970;

al., 2019; Chen, et al., 2019]. The dynamic programming

m is well-designed for most combination optimisation problems.

mbination optimisation problem is such a process in which an

d combination is searched based on the limited number of

nts. A decision is made on a course to discover the best or the

olution among many sequential combinations of the components.