<s>
The	O
Karp	B-Operating_System
–	I-Operating_System
Flatt	I-Operating_System
metric	I-Operating_System
is	O
a	O
measure	O
of	O
parallelization	B-Operating_System
of	O
code	O
in	O
parallel	B-Operating_System
processor	I-Operating_System
systems	O
.	O
</s>
<s>
This	O
metric	B-General_Concept
exists	O
in	O
addition	O
to	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
and	O
Gustafson	B-Operating_System
's	I-Operating_System
law	I-Operating_System
as	O
an	O
indication	O
of	O
the	O
extent	O
to	O
which	O
a	O
particular	O
computer	O
code	O
is	O
parallelized	B-Operating_System
.	O
</s>
<s>
Given	O
a	O
parallel	B-Operating_System
computation	I-Operating_System
exhibiting	O
speedup	B-Operating_System
on	O
processors	O
,	O
where	O
>	O
1	O
,	O
the	O
experimentally	O
determined	O
serial	O
fraction	O
is	O
defined	O
to	O
be	O
the	O
Karp	B-Operating_System
–	I-Operating_System
Flatt	I-Operating_System
Metric	I-Operating_System
viz	O
:	O
</s>
<s>
The	O
lower	O
the	O
value	O
of	O
,	O
the	O
better	O
the	O
parallelization	B-Operating_System
.	O
</s>
<s>
There	O
are	O
many	O
ways	O
to	O
measure	O
the	O
performance	O
of	O
a	O
parallel	B-Operating_System
algorithm	I-Operating_System
running	O
on	O
a	O
parallel	B-Operating_System
processor	I-Operating_System
.	O
</s>
<s>
The	O
Karp	B-Operating_System
–	I-Operating_System
Flatt	I-Operating_System
metric	I-Operating_System
defines	O
a	O
metric	B-General_Concept
which	O
reveals	O
aspects	O
of	O
the	O
performance	O
that	O
are	O
not	O
easily	O
discerned	O
from	O
other	O
metrics	O
.	O
</s>
<s>
A	O
pseudo-	O
"	O
derivation	O
"	O
of	O
sorts	O
follows	O
from	O
Amdahl	B-Operating_System
's	I-Operating_System
Law	I-Operating_System
,	O
which	O
can	O
be	O
written	O
as	O
:	O
</s>
<s>
In	O
terms	O
of	O
the	O
speedup	B-Operating_System
=	O
:	O
</s>
<s>
Solving	O
for	O
the	O
serial	O
fraction	O
,	O
we	O
get	O
the	O
Karp	B-Operating_System
–	I-Operating_System
Flatt	I-Operating_System
metric	I-Operating_System
as	O
above	O
.	O
</s>
<s>
Note	O
that	O
this	O
is	O
not	O
a	O
"	O
derivation	O
"	O
from	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
as	O
the	O
left	O
hand	O
side	O
represents	O
a	O
metric	B-General_Concept
rather	O
than	O
a	O
mathematically	O
derived	O
quantity	O
.	O
</s>
<s>
The	O
treatment	O
above	O
merely	O
shows	O
that	O
the	O
Karp	B-Operating_System
–	I-Operating_System
Flatt	I-Operating_System
metric	I-Operating_System
is	O
consistent	O
with	O
Amdahl	B-Operating_System
's	I-Operating_System
Law	I-Operating_System
.	O
</s>
<s>
While	O
the	O
serial	O
fraction	O
e	O
is	O
often	O
mentioned	O
in	O
computer	B-General_Concept
science	I-General_Concept
literature	O
,	O
it	O
was	O
rarely	O
used	O
as	O
a	O
diagnostic	O
tool	O
the	O
way	O
speedup	B-Operating_System
and	O
efficiency	B-General_Concept
are	O
.	O
</s>
<s>
Karp	O
and	O
Flatt	O
hoped	O
to	O
correct	O
this	O
by	O
proposing	O
this	O
metric	B-General_Concept
.	O
</s>
<s>
This	O
metric	B-General_Concept
addresses	O
the	O
inadequacies	O
of	O
the	O
other	O
laws	O
and	O
quantities	O
used	O
to	O
measure	O
the	O
parallelization	B-Operating_System
of	O
computer	O
code	O
.	O
</s>
<s>
In	O
particular	O
,	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
does	O
not	O
take	O
into	O
account	O
load	B-Application
balancing	I-Application
issues	O
,	O
nor	O
does	O
it	O
take	O
overhead	O
into	O
consideration	O
.	O
</s>
<s>
Using	O
the	O
serial	O
fraction	O
as	O
a	O
metric	B-General_Concept
poses	O
definite	O
advantages	O
over	O
the	O
others	O
,	O
particularly	O
as	O
the	O
number	O
of	O
processors	O
grows	O
.	O
</s>
<s>
For	O
a	O
problem	O
of	O
fixed	O
size	O
,	O
the	O
efficiency	B-General_Concept
of	O
a	O
parallel	B-Operating_System
computation	I-Operating_System
typically	O
decreases	O
as	O
the	O
number	O
of	O
processors	O
increases	O
.	O
</s>
<s>
By	O
using	O
the	O
serial	O
fraction	O
obtained	O
experimentally	O
using	O
the	O
Karp	B-Operating_System
–	I-Operating_System
Flatt	I-Operating_System
metric	I-Operating_System
,	O
we	O
can	O
determine	O
if	O
the	O
efficiency	B-General_Concept
decrease	O
is	O
due	O
to	O
limited	O
opportunities	O
of	O
parallelism	B-Operating_System
or	O
increases	O
in	O
algorithmic	O
or	O
architectural	O
overhead	O
.	O
</s>
