<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
order-maintenance	B-General_Concept
problem	I-General_Concept
involves	O
maintaining	O
a	O
totally	O
ordered	O
set	O
supporting	O
the	O
following	O
operations	O
:	O
</s>
<s>
amortized	B-General_Concept
time	I-General_Concept
with	O
indirection	O
.	O
</s>
<s>
list-labeling	B-General_Concept
problem	I-General_Concept
in	O
which	O
instead	O
of	O
the	O
order( X	O
,	O
</s>
<s>
order-maintenance	B-General_Concept
problem	I-General_Concept
.	O
</s>
<s>
For	O
a	O
list-labeling	B-General_Concept
problem	I-General_Concept
on	O
sets	O
of	O
size	O
up	O
to	O
,	O
the	O
cost	O
of	O
list	O
labeling	O
depends	O
on	O
how	O
large	O
is	O
a	O
function	O
of	O
.	O
</s>
<s>
example	O
,	O
this	O
technique	O
is	O
used	O
in	O
y-fast	B-Data_Structure
tries	I-Data_Structure
.	O
</s>
<s>
of	O
the	O
data	O
structure	O
described	O
above	O
to	O
constant	O
amortized	B-General_Concept
time	I-General_Concept
.	O
</s>
<s>
The	O
labels	O
for	O
this	O
subproblem	O
are	O
taken	O
to	O
be	O
polynomial	O
---	O
say	O
,	O
so	O
that	O
they	O
can	O
be	O
compared	O
in	O
constant	O
time	O
and	O
updated	O
in	O
amortized	B-General_Concept
time	O
.	O
</s>
<s>
Thus	O
,	O
they	O
can	O
be	O
updated	O
in	O
amortized	B-General_Concept
time	I-General_Concept
.	O
</s>
<s>
See	O
the	O
list-labeling	B-General_Concept
problem	I-General_Concept
for	O
details	O
of	O
both	O
solutions	O
.	O
</s>
<s>
Otherwise	O
the	O
labels	O
of	O
their	O
representatives	O
in	O
the	O
first	O
list-labeling	B-General_Concept
problem	I-General_Concept
are	O
compared	O
.	O
</s>
<s>
This	O
case	O
takes	O
amortized	B-General_Concept
time	I-General_Concept
.	O
</s>
<s>
Thus	O
the	O
amortized	B-General_Concept
time	I-General_Concept
per	O
insertion	O
is	O
.	O
</s>
<s>
elements	O
were	O
deleted	O
from	O
the	O
sublist	O
since	O
it	O
was	O
first	O
built	O
we	O
can	O
afford	O
to	O
spend	O
the	O
time	O
,	O
the	O
amortized	B-General_Concept
cost	O
of	O
a	O
deletion	O
is	O
.	O
</s>
