<s>
List	B-Algorithm
scheduling	I-Algorithm
is	O
a	O
greedy	O
algorithm	O
for	O
Identical-machines	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
Then	O
,	O
the	O
resulting	O
schedule	O
is	O
{4,6,8},	O
{5,7},	O
and	O
the	O
makespan	B-Algorithm
is	O
max(18,12 )	O
=	O
18	O
;	O
if	O
m	O
=3	O
,	O
then	O
the	O
resulting	O
schedule	O
is	O
{4,7},	O
{5,8},	O
{6},	O
and	O
the	O
makespan	B-Algorithm
is	O
max(11,13,6 )	O
=	O
13	O
.	O
</s>
<s>
The	O
algorithm	O
always	O
returns	O
a	O
partition	O
of	O
the	O
jobs	O
whose	O
makespan	B-Algorithm
is	O
at	O
most	O
times	O
the	O
optimal	O
makespan	B-Algorithm
.	O
</s>
<s>
This	O
is	O
due	O
to	O
the	O
fact	O
that	O
both	O
the	O
length	O
of	O
the	O
longest	O
job	O
and	O
the	O
average	O
length	O
of	O
all	O
jobs	O
are	O
lower	O
bounds	O
for	O
the	O
optimal	O
makespan	B-Algorithm
.	O
</s>
<s>
The	O
algorithm	O
can	O
be	O
used	O
as	O
an	O
online	B-Algorithm
algorithm	I-Algorithm
,	O
when	O
the	O
order	O
in	O
which	O
the	O
items	O
arrive	O
cannot	O
be	O
controlled	O
.	O
</s>
<s>
Some	O
known	O
list	B-Algorithm
scheduling	I-Algorithm
strategies	O
are	O
:	O
</s>
<s>
Longest-processing-time-first	B-Algorithm
scheduling	I-Algorithm
,	O
or	O
LPT	O
;	O
this	O
variant	O
decreases	O
the	O
approximation	O
ratio	O
to	O
.	O
</s>
<s>
Heterogeneous	B-Algorithm
Earliest	I-Algorithm
Finish	I-Algorithm
Time	I-Algorithm
or	O
HEFT	O
.	O
</s>
<s>
The	O
list	B-Algorithm
scheduling	I-Algorithm
algorithm	O
has	O
several	O
anomalies	O
.	O
</s>
<s>
Then	O
,	O
list	B-Algorithm
scheduling	I-Algorithm
returns	O
the	O
following	O
schedule	O
:	O
</s>
<s>
and	O
the	O
makespan	B-Algorithm
is	O
12	O
.	O
</s>
<s>
and	O
the	O
makespan	B-Algorithm
is	O
16	O
.	O
</s>
<s>
Removing	O
dependencies	O
has	O
enlarged	O
the	O
makespan	B-Algorithm
.	O
</s>
<s>
and	O
the	O
makespan	B-Algorithm
is	O
13	O
.	O
</s>
<s>
Shortening	O
all	O
jobs	O
has	O
enlarged	O
the	O
makespan	B-Algorithm
.	O
</s>
<s>
and	O
the	O
makespan	B-Algorithm
is	O
15	O
.	O
</s>
<s>
Adding	O
a	O
machine	O
has	O
enlarged	O
the	O
makespan	B-Algorithm
.	O
</s>
<s>
Suppose	O
initially	O
we	O
had	O
m1	O
machines	O
and	O
the	O
makespan	B-Algorithm
was	O
t1	O
.	O
</s>
<s>
Now	O
,	O
we	O
have	O
m2	O
machines	O
,	O
the	O
dependencies	O
are	O
the	O
same	O
or	O
relaxed	O
,	O
the	O
job	O
lengths	O
are	O
the	O
same	O
or	O
shorter	O
,	O
the	O
list	O
is	O
the	O
same	O
or	O
different	O
,	O
and	O
the	O
makespan	B-Algorithm
is	O
t2	O
.	O
</s>
