<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
Robertson	O
–	O
Webb	O
(	O
RW	O
)	O
query	O
model	O
is	O
a	O
model	O
of	O
computation	O
used	O
by	O
algorithms	O
for	O
the	O
problem	O
of	O
fair	O
cake-cutting	O
.	O
</s>
<s>
Informally	O
,	O
an	O
Eval	B-Application
query	I-Application
asks	O
an	O
agent	O
to	O
specify	O
his/her	O
value	O
to	O
a	O
given	O
piece	O
of	O
the	O
cake	O
,	O
and	O
a	O
Cut	B-Application
query	I-Application
(	O
also	O
called	O
a	O
Mark	B-Application
query	I-Application
)	O
asks	O
an	O
agent	O
to	O
specify	O
a	O
piece	O
of	O
cake	O
with	O
a	O
given	O
value	O
.	O
</s>
<s>
The	O
Eval	O
and	O
Cut	B-Application
queries	I-Application
were	O
first	O
described	O
in	O
the	O
book	O
of	O
Jack	O
M	O
.	O
Robertson	O
and	O
William	O
A	O
.	O
Webb	O
.	O
</s>
<s>
An	O
eval	B-Application
query	I-Application
:	O
given	O
two	O
real	O
numbers	O
x	O
and	O
y	O
,	O
Evali(x,y )	O
asks	O
agent	O
i	O
to	O
report	O
the	O
value	O
of	O
the	O
interval	O
[x,y],	O
i.e.	O
,	O
vi	O
( [	O
x	O
,	O
y ]	O
)	O
.	O
</s>
<s>
A	O
mark	B-Application
query	I-Application
(	O
also	O
called	O
a	O
cut	B-Application
query	I-Application
)	O
:	O
given	O
two	O
real	O
numbers	O
x	O
and	O
r	O
,	O
Marki(x,r )	O
asks	O
agent	O
i	O
to	O
report	O
some	O
value	O
y	O
such	O
that	O
vi( [x	O
,	O
y ]	O
)	O
=	O
r	O
.	O
</s>
<s>
For	O
example	O
:	O
Last	B-Algorithm
diminisher	I-Algorithm
can	O
be	O
done	O
by	O
O(n2 )	O
RW	O
queries	O
and	O
Even	B-Algorithm
–	I-Algorithm
Paz	I-Algorithm
protocol	I-Algorithm
can	O
be	O
done	O
by	O
O(n log n )	O
RW	O
queries	O
.	O
</s>
<s>
Proportional	B-Algorithm
cake-cutting	I-Algorithm
with	I-Algorithm
different	I-Algorithm
entitlements	I-Algorithm
requires	O
at	O
least	O
Ω( n	O
log(D )	O
)	O
RW	O
queries	O
,	O
where	O
D	O
is	O
the	O
common	O
denominator	O
of	O
the	O
entitlements	O
(	O
in	O
particular	O
,	O
it	O
cannot	O
be	O
found	O
using	O
a	O
bounded	O
number	O
of	O
queries	O
if	O
the	O
entitlements	O
are	O
irrational	O
)	O
.	O
</s>
<s>
Maximin	B-Algorithm
share	I-Algorithm
cake-cutting	O
,	O
when	O
the	O
pieces	O
must	O
be	O
separated	O
by	O
a	O
positive	O
distance	O
,	O
cannot	O
be	O
done	O
using	O
finitely-many	O
RW	O
queries	O
.	O
</s>
<s>
Moreover	O
,	O
even	O
for	O
a	O
single	O
agent	O
,	O
there	O
is	O
no	O
algorithm	O
that	O
computes	O
the	O
agent	O
's	O
maximin-share	B-Algorithm
using	O
finitely-many	O
RW	O
queries	O
.	O
</s>
<s>
When	O
the	O
cake	O
is	O
circular	O
(	O
i.e.	O
,	O
in	O
fair	B-Algorithm
pie-cutting	I-Algorithm
)	O
,	O
it	O
is	O
possible	O
to	O
compute	O
a	O
value	O
between	O
the	O
MMS	O
and	O
the	O
MMS-ε	O
using	O
O( n	O
ε−1	O
)	O
RW	O
queries	O
.	O
</s>
<s>
When	O
the	O
value	O
measure	O
of	O
an	O
agent	O
is	O
not	O
strictly	O
positive	O
(	O
i.e.	O
,	O
there	O
are	O
parts	O
that	O
the	O
agent	O
values	O
at	O
0	O
)	O
,	O
a	O
mark	B-Application
query	I-Application
can	O
,	O
in	O
principle	O
,	O
return	O
infinitely	O
many	O
values	O
.	O
</s>
<s>
If	O
only	O
one	O
of	O
these	O
two	O
variants	O
is	O
given	O
(	O
in	O
addition	O
to	O
the	O
Eval	B-Application
query	I-Application
)	O
,	O
the	O
other	O
variant	O
cannot	O
be	O
computed	O
in	O
finite	O
time	O
.	O
</s>
