<s>
A	O
set	B-Data_Structure
intersection	I-Data_Structure
oracle	I-Data_Structure
(	O
SIO	O
)	O
is	O
a	O
data	B-General_Concept
structure	I-General_Concept
which	O
represents	O
a	O
collection	O
of	O
sets	O
and	O
can	O
quickly	O
answer	O
queries	O
about	O
whether	O
the	O
set	O
intersection	O
of	O
two	O
given	O
sets	O
is	O
non-empty	O
.	O
</s>
<s>
Without	O
any	O
pre-processing	O
,	O
a	O
query	O
can	O
be	O
answered	O
by	O
inserting	O
the	O
elements	O
of	O
Si	O
into	O
a	O
temporary	O
hash	B-Algorithm
table	I-Algorithm
and	O
then	O
checking	O
for	O
each	O
element	O
of	O
Sk	O
whether	O
it	O
is	O
in	O
the	O
hash	B-Algorithm
table	I-Algorithm
.	O
</s>
<s>
Additionally	O
,	O
for	O
each	O
large	O
set	O
,	O
keep	O
a	O
hash	B-Algorithm
table	I-Algorithm
of	O
all	O
its	O
elements	O
.	O
</s>
<s>
Then	O
insert	O
the	O
elements	O
of	O
one	O
of	O
them	O
into	O
a	O
hash	B-Algorithm
table	I-Algorithm
and	O
check	O
the	O
elements	O
of	O
the	O
other	O
one	O
;	O
because	O
the	O
sets	O
are	O
small	O
,	O
the	O
required	O
time	O
is	O
.	O
</s>
<s>
Loop	O
over	O
all	O
elements	O
in	O
the	O
small	O
set	O
and	O
check	O
them	O
against	O
the	O
hash	B-Algorithm
table	I-Algorithm
of	O
the	O
large	O
set	O
.	O
</s>
<s>
The	O
SIO	O
problem	O
can	O
be	O
reduced	O
to	O
the	O
approximate	O
distance	B-Application
oracle	I-Application
(	O
DO	O
)	O
problem	O
,	O
in	O
the	O
following	O
way	O
.	O
</s>
