<s>
The	O
snake-in-the-box	B-Error_Name
problem	O
in	O
graph	O
theory	O
and	O
computer	B-General_Concept
science	I-General_Concept
deals	O
with	O
finding	O
a	O
certain	O
kind	O
of	O
path	O
along	O
the	O
edges	O
of	O
a	O
hypercube	B-Operating_System
.	O
</s>
<s>
In	O
other	O
words	O
,	O
a	O
snake	O
is	O
a	O
connected	O
open	O
path	O
in	O
the	O
hypercube	B-Operating_System
where	O
each	O
node	O
connected	O
with	O
path	O
,	O
with	O
the	O
exception	O
of	O
the	O
head	O
(	O
start	O
)	O
and	O
the	O
tail	O
(	O
finish	O
)	O
,	O
it	O
has	O
exactly	O
two	O
neighbors	O
that	O
are	O
also	O
in	O
the	O
snake	O
.	O
</s>
<s>
The	O
rule	O
for	O
generating	O
a	O
snake	O
is	O
that	O
a	O
node	O
in	O
the	O
hypercube	B-Operating_System
may	O
be	O
visited	O
if	O
it	O
is	O
connected	O
to	O
the	O
current	O
node	O
and	O
it	O
is	O
not	O
a	O
neighbor	O
of	O
any	O
previously	O
visited	O
node	O
in	O
the	O
snake	O
,	O
other	O
than	O
the	O
current	O
node	O
.	O
</s>
<s>
In	O
graph	O
theory	O
terminology	O
,	O
this	O
is	O
called	O
finding	O
the	O
longest	O
possible	O
induced	O
path	O
in	O
a	O
hypercube	B-Operating_System
;	O
it	O
can	O
be	O
viewed	O
as	O
a	O
special	O
case	O
of	O
the	O
induced	O
subgraph	O
isomorphism	O
problem	O
.	O
</s>
<s>
There	O
is	O
a	O
similar	O
problem	O
of	O
finding	O
long	O
induced	O
cycles	O
in	O
hypercubes	B-Operating_System
,	O
called	O
the	O
coil-in-the-box	B-Error_Name
problem	O
.	O
</s>
<s>
The	O
snake-in-the-box	B-Error_Name
problem	O
was	O
first	O
described	O
by	O
,	O
motivated	O
by	O
the	O
theory	O
of	O
error-correcting	B-Error_Name
codes	I-Error_Name
.	O
</s>
<s>
The	O
vertices	O
of	O
a	O
solution	O
to	O
the	O
snake	O
or	O
coil	O
in	O
the	O
box	O
problems	O
can	O
be	O
used	O
as	O
a	O
Gray	B-Device
code	I-Device
that	O
can	O
detect	O
single-bit	O
errors	O
.	O
</s>
<s>
Such	O
codes	O
have	O
applications	O
in	O
electrical	O
engineering	O
,	O
coding	B-Error_Name
theory	I-Error_Name
,	O
and	O
computer	O
network	B-Architecture
topologies	I-Architecture
.	O
</s>
<s>
In	O
these	O
applications	O
,	O
it	O
is	O
important	O
to	O
devise	O
as	O
long	O
a	O
code	O
as	O
is	O
possible	O
for	O
a	O
given	O
dimension	O
of	O
hypercube	B-Operating_System
.	O
</s>
<s>
Some	O
techniques	O
for	O
determining	O
the	O
upper	O
and	O
lower	O
bounds	O
for	O
the	O
snake-in-the-box	B-Error_Name
problem	O
include	O
proofs	O
using	O
discrete	O
mathematics	O
and	O
graph	O
theory	O
,	O
exhaustive	B-Algorithm
search	I-Algorithm
of	O
the	O
search	O
space	O
,	O
and	O
heuristic	B-Algorithm
search	O
utilizing	O
evolutionary	O
techniques	O
.	O
</s>
<s>
For	O
cycles	O
(	O
the	O
coil-in-the-box	B-Error_Name
problem	O
)	O
,	O
a	O
cycle	O
cannot	O
exist	O
in	O
a	O
hypercube	B-Operating_System
of	O
dimension	O
less	O
than	O
two	O
.	O
</s>
