<s>
In	O
computer	O
science	O
,	O
the	O
analysis	B-Operating_System
of	I-Operating_System
parallel	I-Operating_System
algorithms	I-Operating_System
is	O
the	O
process	O
of	O
finding	O
the	O
computational	O
complexity	O
of	O
algorithms	O
executed	O
in	O
parallel	O
–	O
the	O
amount	O
of	O
time	O
,	O
storage	O
,	O
or	O
other	O
resources	O
needed	O
to	O
execute	O
them	O
.	O
</s>
<s>
In	O
many	O
respects	O
,	O
analysis	B-Operating_System
of	I-Operating_System
parallel	I-Operating_System
algorithms	I-Operating_System
is	O
similar	O
to	O
the	O
analysis	B-General_Concept
of	I-General_Concept
sequential	I-General_Concept
algorithms	I-General_Concept
,	O
but	O
is	O
generally	O
more	O
involved	O
because	O
one	O
must	O
reason	O
about	O
the	O
behavior	O
of	O
multiple	O
cooperating	O
threads	O
of	O
execution	O
.	O
</s>
<s>
The	O
depth	O
or	O
span	O
is	O
the	O
length	O
of	O
the	O
longest	O
series	O
of	O
operations	O
that	O
have	O
to	O
be	O
performed	O
sequentially	O
due	O
to	O
data	B-Operating_System
dependencies	I-Operating_System
(	O
the	O
critical	O
path	O
)	O
.	O
</s>
<s>
The	O
depth	O
may	O
also	O
be	O
called	O
the	O
critical	B-Operating_System
path	I-Operating_System
length	I-Operating_System
of	O
the	O
computation	O
.	O
</s>
<s>
Speedup	B-Operating_System
is	O
the	O
gain	O
in	O
speed	O
made	O
by	O
parallel	O
execution	O
compared	O
to	O
sequential	O
execution	O
:	O
.	O
</s>
<s>
When	O
the	O
speedup	B-Operating_System
is	O
for	O
input	O
size	O
(	O
using	O
big	O
O	O
notation	O
)	O
,	O
the	O
speedup	B-Operating_System
is	O
linear	O
,	O
which	O
is	O
optimal	O
in	O
simple	O
models	O
of	O
computation	O
because	O
the	O
work	O
law	O
implies	O
that	O
(	O
super-linear	O
speedup	B-Operating_System
can	O
occur	O
in	O
practice	O
due	O
to	O
memory	B-General_Concept
hierarchy	I-General_Concept
effects	O
)	O
.	O
</s>
<s>
The	O
situation	O
is	O
called	O
perfect	O
linear	B-Operating_System
speedup	I-Operating_System
.	O
</s>
<s>
An	O
algorithm	O
that	O
exhibits	O
linear	B-Operating_System
speedup	I-Operating_System
is	O
said	O
to	O
be	O
scalable	B-Architecture
.	O
</s>
<s>
Efficiency	O
is	O
the	O
speedup	B-Operating_System
per	O
processor	O
,	O
.	O
</s>
<s>
It	O
represents	O
the	O
maximum	O
possible	O
speedup	B-Operating_System
on	O
any	O
number	O
of	O
processors	O
.	O
</s>
<s>
By	O
the	O
span	O
law	O
,	O
the	O
parallelism	O
bounds	O
the	O
speedup	B-Operating_System
:	O
if	O
,	O
then	O
:	O
</s>
<s>
A	O
slackness	O
less	O
than	O
one	O
implies	O
(	O
by	O
the	O
span	O
law	O
)	O
that	O
perfect	O
linear	B-Operating_System
speedup	I-Operating_System
is	O
impossible	O
on	O
processors	O
.	O
</s>
<s>
Analysis	B-Operating_System
of	I-Operating_System
parallel	I-Operating_System
algorithms	I-Operating_System
is	O
usually	O
carried	O
out	O
under	O
the	O
assumption	O
that	O
an	O
unbounded	O
number	O
of	O
processors	O
is	O
available	O
.	O
</s>
