<s>
Single-machine	B-Algorithm
scheduling	I-Algorithm
or	O
single-resource	O
scheduling	O
is	O
an	O
optimization	O
problem	O
in	O
computer	B-General_Concept
science	I-General_Concept
and	O
operations	O
research	O
.	O
</s>
<s>
Single-machine	B-Algorithm
scheduling	I-Algorithm
is	O
a	O
special	O
case	O
of	O
identical-machines	B-Algorithm
scheduling	I-Algorithm
,	O
which	O
is	O
itself	O
a	O
special	O
case	O
of	O
optimal	B-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
In	O
the	O
standard	O
three-field	B-Algorithm
notation	I-Algorithm
for	I-Algorithm
optimal	I-Algorithm
job	I-Algorithm
scheduling	I-Algorithm
problems	I-Algorithm
,	O
the	O
single-machine	O
variant	O
is	O
denoted	O
by	O
1	O
in	O
the	O
first	O
field	O
.	O
</s>
<s>
For	O
example	O
,	O
"	O
1||	O
"	O
is	O
an	O
single-machine	B-Algorithm
scheduling	I-Algorithm
problem	O
with	O
no	O
constraints	O
,	O
where	O
the	O
goal	O
is	O
to	O
minimize	O
the	O
sum	O
of	O
completion	O
times	O
.	O
</s>
<s>
1||	O
can	O
be	O
solved	O
optimally	O
by	O
the	O
Earliest	B-Algorithm
Due	I-Algorithm
Date	I-Algorithm
First	O
rule	O
(	O
EDD	O
)	O
:	O
the	O
jobs	O
are	O
scheduled	O
by	O
ascending	O
order	O
of	O
their	O
deadline	O
.	O
</s>
<s>
The	O
maximum	O
cost	O
can	O
be	O
minimized	O
by	O
a	O
greedy	O
algorithm	O
known	O
as	O
Lawler	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
But	O
in	O
practice	O
,	O
it	O
can	O
be	O
solved	O
using	O
a	O
branch-and-bound	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Single-machine	B-Algorithm
scheduling	I-Algorithm
with	O
deadlines	O
is	O
NP-hard	O
;	O
Sahni	O
presents	O
both	O
exact	O
exponential-time	O
algorithms	O
and	O
a	O
polynomial-time	O
approximation	O
algorithm	O
.	O
</s>
<s>
It	O
is	O
NP-hard	O
,	O
since	O
the	O
special	O
case	O
in	O
which	O
all	O
jobs	O
have	O
the	O
same	O
deadline	O
(	O
denoted	O
by	O
1||	O
)	O
is	O
equivalent	O
to	O
the	O
Knapsack	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
For	O
more	O
details	O
,	O
see	O
the	O
page	O
on	O
interval	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
