<s>
The	O
last	B-Algorithm
diminisher	I-Algorithm
procedure	O
is	O
a	O
procedure	O
for	O
fair	O
cake-cutting	O
.	O
</s>
<s>
Whatever	O
he	O
does	O
,	O
C	O
has	O
the	O
right	O
(	O
without	O
obligation	O
)	O
to	O
diminish	O
still	O
the	O
already	O
diminished	O
(	O
or	O
not	O
diminished	O
)	O
slice	O
,	O
and	O
so	O
on	O
up	O
to	O
N	O
.	O
The	O
rule	O
obliges	O
the	O
"	O
last	B-Algorithm
diminisher	I-Algorithm
"	O
to	O
take	O
as	O
his	O
part	O
the	O
slice	O
he	O
was	O
the	O
last	O
to	O
touch	O
.	O
</s>
<s>
The	O
algorithm	O
simplifies	O
in	O
the	O
degenerate	O
case	O
that	O
all	O
partners	O
have	O
the	O
same	O
preference	O
function	O
because	O
the	O
partner	O
that	O
optimally	O
first	O
cuts	O
a	O
slice	O
will	O
also	O
be	O
its	O
last	B-Algorithm
diminisher	I-Algorithm
.	O
</s>
<s>
;	O
only	O
the	O
"	O
last	B-Algorithm
diminisher	I-Algorithm
"	O
has	O
to	O
actually	O
cut	O
the	O
cake	O
.	O
</s>
<s>
Similar	O
to	O
the	O
last	B-Algorithm
diminisher	I-Algorithm
procedure	O
,	O
it	O
can	O
be	O
used	O
to	O
cut	O
the	O
cake	O
into	O
contiguous	O
parts	O
for	O
each	O
player	O
.	O
</s>
<s>
I.e	O
,	O
a	O
partner	O
that	O
won	O
a	O
piece	O
by	O
being	O
the	O
last	B-Algorithm
diminisher	I-Algorithm
,	O
does	O
not	O
have	O
to	O
leave	O
the	O
game	O
,	O
but	O
may	O
rather	O
stay	O
and	O
participate	O
in	O
further	O
steps	O
.	O
</s>
<s>
The	O
last	B-Algorithm
diminisher	I-Algorithm
procedure	O
has	O
been	O
improved	O
later	O
in	O
many	O
ways	O
.	O
</s>
