<s>
The	O
undercut	B-Algorithm
procedure	I-Algorithm
is	O
a	O
procedure	O
for	O
fair	O
item	O
assignment	O
between	O
two	O
people	O
.	O
</s>
<s>
The	O
undercut	B-Algorithm
procedure	I-Algorithm
requires	O
only	O
the	O
following	O
weak	O
assumptions	O
on	O
the	O
people	O
:	O
</s>
<s>
The	O
undercut	B-Algorithm
procedure	I-Algorithm
can	O
be	O
seen	O
as	O
a	O
generalization	O
of	O
the	O
divide	O
and	O
choose	O
protocol	O
from	O
a	O
divisible	O
resource	O
to	O
a	O
resource	O
with	O
indivisibilities	O
.	O
</s>
<s>
Accordingly	O
,	O
the	O
undercut	B-Algorithm
procedure	I-Algorithm
works	O
with	O
almost-equal-cuts	O
.	O
</s>
<s>
This	O
is	O
not	O
surprising	O
,	O
since	O
the	O
undercut	B-Algorithm
procedure	I-Algorithm
can	O
be	O
used	O
to	O
solve	O
the	O
partition	B-Algorithm
problem	I-Algorithm
:	O
assume	O
both	O
agents	O
have	O
identical	O
and	O
additive	O
valuations	O
and	O
run	O
the	O
undercut	B-Algorithm
procedure	I-Algorithm
;	O
if	O
it	O
finds	O
an	O
envy-free	O
allocation	O
,	O
then	O
this	O
allocation	O
represents	O
an	O
equal	O
partition	O
.	O
</s>
<s>
Since	O
the	O
partition	B-Algorithm
problem	I-Algorithm
is	O
NP-complete	O
,	O
it	O
probably	O
cannot	O
be	O
solved	O
by	O
a	O
polynomial-time	O
algorithm	O
.	O
</s>
<s>
The	O
undercut	B-Algorithm
procedure	I-Algorithm
can	O
also	O
work	O
when	O
the	O
agents	O
have	O
unequal	O
entitlements	O
.	O
</s>
<s>
In	O
the	O
original	O
publication	O
,	O
the	O
undercut	B-Algorithm
procedure	I-Algorithm
is	O
preceded	O
by	O
the	O
following	O
generation	O
phase	O
:	O
</s>
<s>
The	O
undercut	B-Algorithm
procedure	I-Algorithm
described	O
above	O
is	O
then	O
executed	O
only	O
on	O
the	O
contested	O
pile	O
.	O
</s>
<s>
Indeed	O
,	O
it	O
can	O
be	O
found	O
by	O
the	O
bare	O
undercut	B-Algorithm
procedure	I-Algorithm
,	O
since	O
the	O
partition	O
( {	O
w	O
,	O
z}	O
,	O
 { x , y } 	O
)	O
is	O
an	O
almost-equal-cut	O
for	O
Alice	O
but	O
not	O
for	O
George	O
,	O
and	O
George	O
would	O
accept	O
this	O
partition	O
.	O
</s>
