<s>
Domination	B-Algorithm
analysis	I-Algorithm
of	O
an	O
approximation	B-Algorithm
algorithm	I-Algorithm
is	O
a	O
way	O
to	O
estimate	O
its	O
performance	O
,	O
introduced	O
by	O
Glover	O
and	O
Punnen	O
in	O
1997	O
.	O
</s>
<s>
Unlike	O
the	O
classical	O
approximation	B-Algorithm
ratio	I-Algorithm
analysis	O
,	O
which	O
compares	O
the	O
numerical	O
quality	O
of	O
a	O
calculated	O
solution	O
with	O
that	O
of	O
an	O
optimal	O
solution	O
,	O
domination	B-Algorithm
analysis	I-Algorithm
involves	O
examining	O
the	O
rank	O
of	O
the	O
calculated	O
solution	O
in	O
the	O
sorted	O
order	O
of	O
all	O
possible	O
solutions	O
.	O
</s>
<s>
In	O
this	O
style	O
of	O
analysis	O
,	O
an	O
algorithm	O
is	O
said	O
to	O
have	O
dominance	B-Algorithm
number	I-Algorithm
or	O
domination	O
number	O
K	O
,	O
if	O
there	O
exists	O
a	O
subset	O
of	O
K	O
different	O
solutions	O
to	O
the	O
problem	O
among	O
which	O
the	O
algorithm	O
's	O
output	O
is	O
the	O
best	O
.	O
</s>
<s>
Domination	B-Algorithm
analysis	I-Algorithm
can	O
also	O
be	O
expressed	O
using	O
a	O
domination	O
ratio	O
,	O
which	O
is	O
the	O
fraction	O
of	O
the	O
solution	O
space	O
that	O
is	O
no	O
better	O
than	O
the	O
given	O
solution	O
;	O
this	O
number	O
always	O
lies	O
within	O
the	O
interval	O
[0,1],	O
with	O
larger	O
numbers	O
indicating	O
better	O
solutions	O
.	O
</s>
<s>
Domination	B-Algorithm
analysis	I-Algorithm
is	O
most	O
commonly	O
applied	O
to	O
problems	O
for	O
which	O
the	O
total	O
number	O
of	O
possible	O
solutions	O
is	O
known	O
and	O
for	O
which	O
exact	O
solution	O
is	O
difficult	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
the	O
Traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
,	O
there	O
are	O
(	O
n-1	O
)	O
!	O
</s>
<s>
If	O
an	O
algorithm	O
can	O
be	O
shown	O
to	O
have	O
dominance	B-Algorithm
number	I-Algorithm
close	O
to	O
(	O
n-1	O
)	O
!,	O
or	O
equivalently	O
to	O
have	O
domination	O
ratio	O
close	O
to	O
1	O
,	O
then	O
it	O
can	O
be	O
taken	O
as	O
preferable	O
to	O
an	O
algorithm	O
with	O
lower	O
dominance	B-Algorithm
number	I-Algorithm
.	O
</s>
<s>
If	O
it	O
is	O
possible	O
to	O
efficiently	O
find	O
random	O
samples	O
of	O
a	O
problem	O
's	O
solution	O
space	O
,	O
as	O
it	O
is	O
in	O
the	O
Traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
,	O
then	O
it	O
is	O
straightforward	O
for	O
a	O
randomized	B-General_Concept
algorithm	I-General_Concept
to	O
find	O
a	O
solution	O
that	O
with	O
high	O
probability	O
has	O
high	O
domination	O
ratio	O
:	O
simply	O
construct	O
a	O
set	O
of	O
samples	O
and	O
select	O
the	O
best	O
solution	O
from	O
among	O
them	O
.	O
</s>
<s>
The	O
dominance	B-Algorithm
number	I-Algorithm
described	O
here	O
should	O
not	O
be	O
confused	O
with	O
the	O
domination	O
number	O
of	O
a	O
graph	O
,	O
which	O
refers	O
to	O
the	O
number	O
of	O
vertices	O
in	O
the	O
smallest	O
dominating	O
set	O
of	O
the	O
graph	O
.	O
</s>
<s>
Recently	O
,	O
a	O
growing	O
number	O
of	O
articles	O
in	O
which	O
domination	B-Algorithm
analysis	I-Algorithm
has	O
been	O
applied	O
to	O
assess	O
the	O
performance	O
of	O
heuristics	O
has	O
appeared	O
.	O
</s>
<s>
This	O
kind	O
of	O
analysis	O
may	O
be	O
seen	O
as	O
competing	O
with	O
the	O
classical	O
approximation	B-Algorithm
ratio	I-Algorithm
analysis	O
tradition	O
.	O
</s>
