<s>
In	O
peer-to-peer	O
networks	O
,	O
Koorde	B-Algorithm
is	O
a	O
distributed	B-Operating_System
hash	I-Operating_System
table	I-Operating_System
(	O
DHT	O
)	O
system	O
based	O
on	O
the	O
Chord	B-Application
DHT	I-Application
and	O
the	O
De	O
Bruijn	O
graph	O
(	O
De	B-Language
Bruijn	I-Language
sequence	I-Language
)	O
.	O
</s>
<s>
Inheriting	O
the	O
simplicity	O
of	O
Chord	B-Application
,	O
Koorde	B-Algorithm
meets	O
hops	O
per	O
node	B-Protocol
(	O
where	O
is	O
the	O
number	O
of	O
nodes	O
in	O
the	O
DHT	O
)	O
,	O
and	O
hops	O
per	O
lookup	O
request	O
with	O
neighbors	O
per	O
node	B-Protocol
.	O
</s>
<s>
The	O
Chord	B-Application
concept	O
is	O
based	O
on	O
a	O
wide	O
range	O
of	O
identifiers	B-Protocol
(	O
e.g.	O
</s>
<s>
2	O
)	O
in	O
a	O
structure	O
of	O
a	O
ring	B-Architecture
where	O
an	O
identifier	O
can	O
stand	O
for	O
both	O
node	B-Protocol
and	O
data	O
.	O
</s>
<s>
Node-successor	O
is	O
responsible	O
for	O
the	O
whole	O
range	O
of	O
IDs	O
between	O
itself	O
and	O
its	O
predecessor	O
.	O
</s>
<s>
Koorde	B-Algorithm
is	O
based	O
on	O
Chord	B-Application
but	O
also	O
on	O
the	O
De	O
Bruijn	O
graph	O
(	O
De	B-Language
Bruijn	I-Language
sequence	I-Language
)	O
.	O
</s>
<s>
In	O
a	O
-dimensional	O
de	O
Bruijn	O
graph	O
,	O
there	O
are	O
nodes	O
,	O
each	O
of	O
which	O
has	O
a	O
unique	O
ID	B-Protocol
with	O
bits	O
.	O
</s>
<s>
The	O
node	B-Protocol
with	O
ID	B-Protocol
is	O
connected	O
to	O
nodes	O
and	O
.	O
</s>
<s>
Thanks	O
to	O
this	O
property	O
,	O
the	O
routing	B-Protocol
algorithm	I-Protocol
can	O
route	O
to	O
any	O
destination	O
in	O
hops	O
by	O
successively	O
"	O
shifting	O
in	O
"	O
the	O
bits	O
of	O
the	O
destination	O
ID	B-Protocol
but	O
only	O
if	O
the	O
dimensions	O
of	O
the	O
distance	O
between	O
and	O
are	O
equal	O
.	O
</s>
<s>
Routing	B-Protocol
a	O
message	O
from	O
node	B-Protocol
to	O
node	B-Protocol
is	O
accomplished	O
by	O
taking	O
the	O
number	O
and	O
shifting	O
in	O
the	O
bits	O
of	O
one	O
at	O
a	O
time	O
until	O
the	O
number	O
has	O
been	O
replaced	O
by	O
.	O
</s>
<s>
Each	O
shift	O
corresponds	O
to	O
a	O
routing	B-Protocol
hop	O
to	O
the	O
next	O
intermediate	O
address	O
;	O
the	O
hop	O
is	O
valid	O
because	O
each	O
node	B-Protocol
's	O
neighbors	O
are	O
the	O
two	O
possible	O
outcomes	O
of	O
shifting	O
a	O
0	O
or	O
1	O
onto	O
its	O
own	O
address	O
.	O
</s>
<s>
Because	O
of	O
the	O
structure	O
of	O
de	O
Bruijn	O
graphs	O
,	O
when	O
the	O
last	O
bit	O
of	O
has	O
been	O
shifted	O
,	O
the	O
query	O
will	O
be	O
at	O
node	B-Protocol
.	O
</s>
<s>
Node	B-Protocol
responds	O
whether	O
key	O
exists	O
.	O
</s>
<s>
For	O
example	O
,	O
when	O
a	O
message	O
needs	O
to	O
be	O
routed	B-Protocol
from	O
node	B-Protocol
2	O
(	O
which	O
is	O
)	O
to	O
6	O
(	O
which	O
is	O
)	O
,	O
the	O
steps	O
are	O
following	O
:	O
</s>
<s>
Node	B-Protocol
2	O
routes	O
the	O
message	O
to	O
Node	B-Protocol
5	O
(	O
using	O
its	O
connection	O
to	O
)	O
,	O
shifts	O
the	O
bits	O
left	O
and	O
puts	O
as	O
the	O
youngest	O
bit	O
(	O
right	O
side	O
)	O
.	O
</s>
<s>
Node	B-Protocol
5	O
routes	O
the	O
message	O
to	O
Node	B-Protocol
3	O
(	O
using	O
its	O
connection	O
to	O
)	O
,	O
shifts	O
the	O
bits	O
left	O
and	O
puts	O
as	O
the	O
youngest	O
bit	O
(	O
right	O
side	O
)	O
.	O
</s>
<s>
Node	B-Protocol
3	O
routes	O
the	O
message	O
to	O
Node	B-Protocol
6	O
(	O
using	O
its	O
connection	O
to	O
)	O
,	O
shifts	O
the	O
bits	O
left	O
and	O
puts	O
as	O
the	O
youngest	O
bit	O
(	O
right	O
side	O
)	O
.	O
</s>
<s>
The	O
-dimensional	O
de	O
Bruijn	O
can	O
be	O
generalized	O
to	O
base	O
,	O
in	O
which	O
case	O
node	B-Protocol
is	O
connected	O
to	O
nodes	O
,	O
.	O
</s>
<s>
Koorde	B-Algorithm
node	B-Protocol
maintains	O
pointers	O
to	O
consecutive	O
nodes	O
beginning	O
at	O
the	O
predecessor	O
of	O
.	O
</s>
<s>
Each	O
de	O
Bruijn	O
routing	B-Protocol
step	O
can	O
be	O
emulated	O
with	O
an	O
expected	O
constant	O
number	O
of	O
messages	O
,	O
so	O
routing	B-Protocol
uses	O
expected	O
hops	O
-	O
For	O
,	O
we	O
get	O
degree	O
and	O
diameter	O
.	O
</s>
<s>
Pseudocode	B-Language
for	O
the	O
Koorde	B-Algorithm
lookup	O
algorithm	O
at	O
node	B-Protocol
:	O
</s>
