<s>
Retiming	B-Application
is	O
the	O
technique	O
of	O
moving	O
the	O
structural	O
location	O
of	O
latches	B-General_Concept
or	O
registers	O
in	O
a	O
digital	O
circuit	O
to	O
improve	O
its	O
performance	O
,	O
area	O
,	O
and/or	O
power	O
characteristics	O
in	O
such	O
a	O
way	O
that	O
preserves	O
its	O
functional	O
behavior	O
at	O
its	O
outputs	O
.	O
</s>
<s>
Retiming	B-Application
was	O
first	O
described	O
by	O
Charles	O
E	O
.	O
Leiserson	O
and	O
James	O
B	O
.	O
Saxe	O
in	O
1983	O
.	O
</s>
<s>
The	O
technique	O
uses	O
a	O
directed	O
graph	O
where	O
the	O
vertices	O
represent	O
asynchronous	O
combinational	O
blocks	O
and	O
the	O
directed	O
edges	O
represent	O
a	O
series	O
of	O
registers	O
or	O
latches	B-General_Concept
(	O
the	O
number	O
of	O
registers	O
or	O
latches	B-General_Concept
can	O
be	O
zero	O
)	O
.	O
</s>
<s>
In	O
all	O
cases	O
,	O
if	O
the	O
rules	O
are	O
followed	O
,	O
the	O
circuit	O
will	O
have	O
the	O
same	O
functional	O
behavior	O
as	O
it	O
did	O
before	O
retiming	B-Application
.	O
</s>
<s>
The	O
initial	O
formulation	O
of	O
the	O
retiming	B-Application
problem	O
as	O
described	O
by	O
Leiserson	O
and	O
Saxe	O
is	O
as	O
follows	O
.	O
</s>
<s>
The	O
goal	O
in	O
retiming	B-Application
is	O
to	O
compute	O
an	O
integer	O
lag	O
value	O
for	O
each	O
vertex	O
such	O
that	O
the	O
retimed	O
weight	O
of	O
every	O
edge	O
is	O
non-negative	O
.	O
</s>
<s>
The	O
most	O
common	O
use	O
of	O
retiming	B-Application
is	O
to	O
minimize	O
the	O
clock	O
period	O
.	O
</s>
<s>
The	O
linear	B-Algorithm
program	I-Algorithm
below	O
is	O
feasible	O
if	O
and	O
only	O
if	O
is	O
a	O
feasible	O
clock	O
period	O
.	O
</s>
<s>
The	O
dual	O
of	O
this	O
program	O
is	O
a	O
minimum	B-Algorithm
cost	I-Algorithm
circulation	I-Algorithm
problem	I-Algorithm
,	O
which	O
can	O
be	O
solved	O
efficiently	O
as	O
a	O
network	O
problem	O
.	O
</s>
<s>
Alternatively	O
,	O
feasibility	O
of	O
a	O
clock	O
period	O
can	O
be	O
expressed	O
as	O
a	O
mixed-integer	O
linear	B-Algorithm
program	I-Algorithm
(	O
MILP	O
)	O
.	O
</s>
<s>
Retiming	B-Application
has	O
found	O
industrial	O
use	O
,	O
albeit	O
sporadic	O
.	O
</s>
<s>
Some	O
retimings	B-Application
may	O
also	O
require	O
complicated	O
initialization	O
logic	O
to	O
have	O
the	O
circuit	O
start	O
in	O
an	O
identical	O
initial	O
state	O
.	O
</s>
<s>
Whereas	O
retiming	B-Application
relocates	O
the	O
structural	O
position	O
of	O
the	O
registers	O
,	O
clock	O
skew	O
scheduling	O
moves	O
their	O
temporal	O
position	O
by	O
scheduling	O
the	O
arrival	O
time	O
of	O
the	O
clock	O
signals	O
.	O
</s>
