<s>
In	O
computer	B-Architecture
networking	I-Architecture
,	O
hypercube	B-Operating_System
networks	O
are	O
a	O
type	O
of	O
network	B-Architecture
topology	I-Architecture
used	O
to	O
connect	O
multiple	O
processors	O
with	O
memory	B-General_Concept
modules	I-General_Concept
and	O
accurately	O
route	B-Protocol
data	I-Protocol
.	O
</s>
<s>
Hypercube	B-Operating_System
networks	O
consist	O
of	O
nodes	O
,	O
which	O
form	O
the	O
vertices	O
of	O
squares	O
to	O
create	O
an	O
internetwork	B-Architecture
connection	O
.	O
</s>
<s>
A	O
hypercube	B-Operating_System
is	O
basically	O
a	O
multidimensional	O
mesh	B-Architecture
network	I-Architecture
with	O
two	O
nodes	O
in	O
each	O
dimension	O
.	O
</s>
<s>
Due	O
to	O
similarity	O
,	O
such	O
topologies	B-Architecture
are	O
usually	O
grouped	O
into	O
a	O
-ary	O
-dimensional	O
mesh	B-Architecture
topology	I-Architecture
family	O
,	O
where	O
represents	O
the	O
number	O
of	O
dimensions	O
and	O
represents	O
the	O
number	O
of	O
nodes	O
in	O
each	O
dimension	O
.	O
</s>
<s>
Hypercube	B-Operating_System
interconnection	O
network	B-Architecture
is	O
formed	O
by	O
connecting	O
N	O
nodes	O
that	O
can	O
be	O
expressed	O
as	O
a	O
power	O
of	O
2	O
.	O
</s>
<s>
This	O
means	O
if	O
the	O
network	B-Architecture
has	O
N	O
nodes	O
it	O
can	O
be	O
expressed	O
as	O
:	O
</s>
<s>
where	O
m	O
is	O
the	O
number	O
of	O
bits	O
that	O
are	O
required	O
to	O
label	O
the	O
nodes	O
in	O
the	O
network	B-Architecture
.	O
</s>
<s>
So	O
,	O
if	O
there	O
are	O
4	O
nodes	O
in	O
the	O
network	B-Architecture
,	O
2	O
bits	O
are	O
needed	O
to	O
represent	O
all	O
the	O
nodes	O
in	O
the	O
network	B-Architecture
.	O
</s>
<s>
The	O
network	B-Architecture
is	O
constructed	O
by	O
connecting	O
the	O
nodes	O
that	O
just	O
differ	O
by	O
one	O
bit	O
in	O
their	O
binary	O
representation	O
.	O
</s>
<s>
A	O
3D	O
hypercube	B-Operating_System
internetwork	B-Architecture
would	O
be	O
a	O
cube	O
with	O
8	O
nodes	O
and	O
12	O
edges	O
.	O
</s>
<s>
A	O
4D	O
hypercube	B-Operating_System
network	B-Architecture
can	O
be	O
created	O
by	O
duplicating	O
two	O
3D	O
networks	O
,	O
and	O
adding	O
a	O
most	O
significant	O
bit	O
.	O
</s>
<s>
The	O
new	O
added	O
bit	O
should	O
be	O
‘	O
0’	O
for	O
one	O
3D	O
hypercube	B-Operating_System
and	O
‘	O
1’	O
for	O
the	O
other	O
3D	O
hypercube	B-Operating_System
.	O
</s>
<s>
The	O
corners	O
of	O
the	O
respective	O
one-bit	O
changed	O
MSBs	O
are	O
connected	O
to	O
create	O
the	O
higher	O
hypercube	B-Operating_System
network	B-Architecture
.	O
</s>
<s>
This	O
method	O
can	O
be	O
used	O
to	O
construct	O
any	O
m-bit	O
represented	O
hypercube	B-Operating_System
with	O
(	O
m-1	O
)	O
-bit	O
represented	O
hypercube	B-Operating_System
.	O
</s>
<s>
Routing	B-Protocol
method	O
for	O
a	O
hypercube	B-Operating_System
network	B-Architecture
is	O
referred	O
to	O
as	O
E-Cube	O
routing	B-Protocol
.	O
</s>
<s>
The	O
distance	O
between	O
two	O
nodes	O
in	O
the	O
network	B-Architecture
can	O
be	O
given	O
by	O
Hamming	O
weight	O
of	O
(	O
number	O
of	O
ones	O
in	O
)	O
the	O
XOR-operation	O
between	O
their	O
respective	O
binary	O
labels	O
.	O
</s>
<s>
The	O
distance	O
between	O
Node	B-Protocol
1	O
(	O
represented	O
as	O
‘	O
01’	O
)	O
and	O
Node	B-Protocol
2	O
(	O
represented	O
as	O
‘	O
10’	O
)	O
in	O
the	O
network	B-Architecture
given	O
by	O
:	O
</s>
<s>
E-Cube	O
routing	B-Protocol
is	O
a	O
static	B-Protocol
routing	I-Protocol
method	O
that	O
employs	O
XY-routing	O
algorithm	O
.	O
</s>
<s>
This	O
is	O
commonly	O
referred	O
to	O
as	O
Deterministic	B-General_Concept
,	O
Dimension	O
Ordered	O
Routing	B-Protocol
model	O
.	O
</s>
<s>
E-Cube	O
routing	B-Protocol
works	O
by	O
traversing	O
the	O
network	B-Architecture
in	O
the	O
kth	O
dimension	O
where	O
k	O
is	O
the	O
least	O
significant	O
non-zero	O
bit	O
in	O
the	O
result	O
of	O
calculating	O
distance	O
.	O
</s>
<s>
Figuring	O
out	O
which	O
way	O
to	O
go	O
for	O
a	O
‘	O
0’	O
or	O
‘	O
1’	O
is	O
determined	O
by	O
XY	O
routing	B-Protocol
algorithm	I-Protocol
.	O
</s>
<s>
Different	O
measures	O
of	O
performance	O
are	O
used	O
to	O
evaluate	O
the	O
efficiency	O
of	O
a	O
hypercube	B-Operating_System
network	B-Architecture
connection	O
against	O
various	O
other	O
network	B-Architecture
topologies	I-Architecture
.	O
</s>
<s>
This	O
defines	O
the	O
number	O
of	O
immediately	O
adjacent	O
nodes	O
to	O
a	O
particular	O
node	B-Protocol
.	O
</s>
<s>
In	O
case	O
of	O
a	O
hypercube	B-Operating_System
the	O
degree	O
is	O
m	O
.	O
</s>
<s>
This	O
basically	O
gives	O
us	O
the	O
delay	O
in	O
transmitting	O
a	O
message	O
across	O
a	O
network	B-Architecture
.	O
</s>
<s>
In	O
case	O
of	O
a	O
hypercube	B-Operating_System
the	O
diameter	O
is	O
m	O
.	O
</s>
<s>
In	O
case	O
of	O
Hypercubes	B-Operating_System
the	O
average	O
distance	O
is	O
given	O
as	O
m/2	O
.	O
</s>
<s>
This	O
is	O
the	O
lowest	O
number	O
of	O
wires	O
that	O
you	O
should	O
cut	O
in	O
order	O
to	O
divide	O
the	O
network	B-Architecture
into	O
two	O
equal	O
halves	O
.	O
</s>
<s>
It	O
is	O
given	O
as	O
2m-1	O
for	O
Hypercubes	B-Operating_System
.	O
</s>
