<s>
The	O
r-to-1	O
collision	B-Algorithm
problem	I-Algorithm
is	O
an	O
important	O
theoretical	O
problem	O
in	O
complexity	O
theory	O
,	O
quantum	B-Architecture
computing	I-Architecture
,	O
and	O
computational	O
mathematics	O
.	O
</s>
<s>
The	O
collision	B-Algorithm
problem	I-Algorithm
most	O
often	O
refers	O
to	O
the	O
2-to-1	O
version	O
:	O
given	O
even	O
and	O
a	O
function	O
,	O
we	O
are	O
promised	O
that	O
f	O
is	O
either	O
1-to-1	O
or	O
2-to-1	O
.	O
</s>
<s>
The	O
BHT	B-Algorithm
algorithm	I-Algorithm
,	O
which	O
uses	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
solves	O
this	O
problem	O
optimally	O
by	O
only	O
making	O
queries	O
to	O
f	O
.	O
</s>
