<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
greedy	B-Algorithm
number	I-Algorithm
partitioning	I-Algorithm
is	O
a	O
class	O
of	O
greedy	B-Algorithm
algorithms	I-Algorithm
for	O
multiway	B-Algorithm
number	I-Algorithm
partitioning	I-Algorithm
.	O
</s>
<s>
Greedy	B-Algorithm
algorithms	I-Algorithm
process	O
the	O
numbers	O
sequentially	O
,	O
and	O
insert	O
the	O
next	O
number	O
into	O
a	O
bin	O
in	O
which	O
the	O
sum	O
of	O
numbers	O
is	O
currently	O
smallest	O
.	O
</s>
<s>
The	O
simplest	O
greedy	O
partitioning	O
algorithm	O
is	O
called	O
list	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
This	O
heuristic	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>
An	O
improved	O
greedy	B-Algorithm
algorithm	I-Algorithm
is	O
called	O
LPT	B-Algorithm
scheduling	I-Algorithm
.	O
</s>
<s>
Since	O
it	O
needs	O
to	O
pre-order	O
the	O
inputs	O
,	O
it	O
can	O
be	O
used	O
only	O
as	O
an	O
offline	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
See	O
LPT	B-Algorithm
scheduling	I-Algorithm
for	O
more	O
details	O
.	O
</s>
<s>
The	O
complete	O
greedy	B-Algorithm
algorithm	I-Algorithm
(	O
CGA	O
)	O
is	O
an	O
exact	B-Algorithm
algorithm	I-Algorithm
,	O
i.e.	O
,	O
it	O
always	O
finds	O
an	O
optimal	O
solution	O
.	O
</s>
<s>
Traversing	O
the	O
tree	O
in	O
depth-first	B-Algorithm
order	O
requires	O
only	O
O(n )	O
space	O
,	O
but	O
might	O
take	O
O(kn )	O
time	O
.	O
</s>
<s>
The	O
runtime	O
can	O
be	O
improved	O
by	O
using	O
the	O
greedy	B-Algorithm
heuristic	I-Algorithm
:	O
in	O
each	O
level	O
,	O
develop	O
first	O
the	O
branch	O
in	O
which	O
the	O
current	O
number	O
is	O
put	O
in	O
the	O
set	O
with	O
the	O
smallest	O
sum	O
.	O
</s>
<s>
The	O
natural	O
generalization	O
of	O
the	O
greedy	B-Algorithm
number	I-Algorithm
partitioning	I-Algorithm
algorithm	O
is	O
the	O
envy-graph	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Moreover	O
,	O
if	O
the	O
instance	O
is	O
ordered	O
(	O
-	O
all	O
agents	O
rank	O
the	O
items	O
in	O
the	O
same	O
order	O
)	O
,	O
then	O
the	O
outcome	O
is	O
EFX	O
,	O
and	O
guarantees	O
to	O
each	O
agent	O
at	O
least	O
of	O
his	O
maximin	B-Algorithm
share	I-Algorithm
.	O
</s>
