<s>
In	O
mathematics	O
,	O
an	O
interval	B-Algorithm
contractor	I-Algorithm
(	O
or	O
contractor	O
for	O
short	O
)	O
associated	O
to	O
a	O
set	O
X	O
is	O
an	O
operator	O
C	O
which	O
associates	O
to	O
a	O
box	O
 [ x ] 	O
in	O
Rn	O
another	O
box	O
C( [x]	O
)	O
of	O
Rn	O
such	O
that	O
the	O
two	O
following	O
properties	O
are	O
always	O
satisfied	O
:	O
</s>
<s>
contractor	O
associated	O
to	O
the	O
set	O
X	O
of	O
all	O
x	O
which	O
satisfy	O
the	O
constraint	B-Algorithm
.	O
</s>
<s>
Contractors	O
make	O
it	O
possible	O
to	O
improve	O
the	O
efficiency	O
of	O
branch-and-bound	B-Algorithm
algorithms	I-Algorithm
classically	O
used	O
in	O
interval	B-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
Most	O
of	O
them	O
are	O
based	O
on	O
interval	B-Algorithm
arithmetic	I-Algorithm
.	O
</s>
<s>
The	O
principle	O
is	O
to	O
evaluate	O
f(x )	O
using	O
interval	B-Algorithm
arithmetic	I-Algorithm
(	O
this	O
is	O
the	O
forward	O
step	O
)	O
.	O
</s>
<s>
by	O
taking	O
each	O
forward	O
constraint	B-Algorithm
in	O
the	O
reverse	O
order	O
and	O
isolating	O
each	O
variable	O
on	O
the	O
right	O
hand	O
side	O
.	O
</s>
<s>
is	O
obtained	O
by	O
evaluating	O
the	O
forward	O
and	O
the	O
backward	O
constraints	O
using	O
interval	B-Algorithm
analysis	I-Algorithm
.	O
</s>
