<s>
The	O
Luleå	B-Protocol
algorithm	I-Protocol
of	O
computer	B-General_Concept
science	I-General_Concept
,	O
designed	O
by	O
,	O
is	O
a	O
technique	O
for	O
storing	O
and	O
searching	O
internet	O
routing	B-Protocol
tables	I-Protocol
efficiently	O
.	O
</s>
<s>
The	O
key	O
task	O
to	O
be	O
performed	O
in	O
internet	O
routing	O
is	O
to	O
match	O
a	O
given	O
IPv4	B-Protocol
address	B-Protocol
(	O
viewed	O
as	O
a	O
sequence	O
of	O
32	O
bits	O
)	O
to	O
the	O
longest	O
prefix	O
of	O
the	O
address	B-Protocol
for	O
which	O
routing	O
information	O
is	O
available	O
.	O
</s>
<s>
This	O
prefix	O
matching	O
problem	O
may	O
be	O
solved	O
by	O
a	O
trie	B-General_Concept
,	O
but	O
trie	B-General_Concept
structures	O
use	O
a	O
significant	O
amount	O
of	O
space	O
(	O
a	O
node	B-Data_Structure
for	O
each	O
bit	O
of	O
each	O
address	B-Protocol
)	O
and	O
searching	O
them	O
requires	O
traversing	O
a	O
sequence	O
of	O
nodes	O
with	O
length	O
proportional	O
to	O
the	O
number	O
of	O
bits	O
in	O
the	O
address	B-Protocol
.	O
</s>
<s>
The	O
Luleå	B-Protocol
algorithm	I-Protocol
shortcuts	O
this	O
process	O
by	O
storing	O
only	O
the	O
nodes	O
at	O
three	O
levels	O
of	O
the	O
trie	B-General_Concept
structure	O
,	O
rather	O
than	O
storing	O
the	O
entire	O
trie	B-General_Concept
.	O
</s>
<s>
Before	O
building	O
the	O
Luleå	O
trie	B-General_Concept
,	O
the	O
routing	B-Protocol
table	I-Protocol
entries	O
need	O
to	O
be	O
preprocessed	O
.	O
</s>
<s>
It	O
is	O
also	O
required	O
that	O
the	O
prefix	B-General_Concept
tree	I-General_Concept
is	O
complete	O
.	O
</s>
<s>
If	O
there	O
is	O
no	O
routing	B-Protocol
table	I-Protocol
entries	O
for	O
the	O
entire	O
address	B-Protocol
space	O
,	O
it	O
must	O
be	O
completed	O
by	O
adding	O
dummy	O
entries	O
,	O
which	O
only	O
carries	O
the	O
information	O
that	O
no	O
route	O
is	O
present	O
for	O
that	O
range	O
.	O
</s>
<s>
This	O
enables	O
the	O
simplified	O
lookup	O
in	O
the	O
Luleå	O
trie	B-General_Concept
(	O
)	O
.	O
</s>
<s>
The	O
main	O
advantage	O
of	O
the	O
Luleå	B-Protocol
algorithm	I-Protocol
for	O
the	O
routing	O
task	O
is	O
that	O
it	O
uses	O
very	O
little	O
memory	O
,	O
averaging	O
4	O
–	O
5	O
bytes	O
per	O
entry	O
for	O
large	O
routing	B-Protocol
tables	I-Protocol
.	O
</s>
<s>
However	O
,	O
it	O
has	O
the	O
disadvantage	O
that	O
it	O
cannot	O
be	O
modified	O
easily	O
:	O
small	O
changes	O
to	O
the	O
routing	B-Protocol
table	I-Protocol
may	O
require	O
most	O
or	O
all	O
of	O
the	O
data	O
structure	O
to	O
be	O
reconstructed	O
.	O
</s>
<s>
A	O
bit	B-Data_Structure
vector	I-Data_Structure
consisting	O
of	O
216	O
=	O
65,536	O
bits	O
,	O
with	O
one	O
entry	O
for	O
each	O
16-bit	O
prefix	O
of	O
an	O
IPv4	B-Protocol
address	B-Protocol
.	O
</s>
<s>
A	O
bit	O
in	O
this	O
table	O
is	O
set	O
to	O
one	O
if	O
there	O
is	O
routing	O
information	O
associated	O
with	O
that	O
prefix	O
or	O
with	O
a	O
longer	O
sequence	O
beginning	O
with	O
that	O
prefix	O
,	O
or	O
if	O
the	O
given	O
prefix	O
is	O
the	O
first	O
one	O
associated	O
with	O
routing	O
information	O
at	O
some	O
higher	O
level	O
of	O
the	O
trie	B-General_Concept
;	O
otherwise	O
it	O
is	O
set	O
to	O
zero	O
.	O
</s>
<s>
An	O
array	O
of	O
16-bit	O
words	O
for	O
each	O
nonzero	O
bit	O
in	O
the	O
bit	B-Data_Structure
vector	I-Data_Structure
.	O
</s>
<s>
An	O
array	O
of	O
"	O
base	O
indexes	O
"	O
,	O
one	O
for	O
each	O
consecutive	O
subsequence	O
of	O
64	O
bits	O
in	O
the	O
bit	B-Data_Structure
vector	I-Data_Structure
,	O
pointing	O
to	O
the	O
first	O
datum	O
associated	O
with	O
a	O
nonzero	O
bit	O
in	O
that	O
subsequence	O
.	O
</s>
<s>
An	O
array	O
of	O
"	O
code	O
words	O
"	O
,	O
one	O
for	O
each	O
consecutive	O
subsequence	O
of	O
16	O
bits	O
in	O
the	O
bit	B-Data_Structure
vector	I-Data_Structure
.	O
</s>
<s>
Because	O
the	O
prefix	B-General_Concept
tree	I-General_Concept
is	O
required	O
to	O
be	O
complete	O
,	O
there	O
can	O
only	O
exist	O
a	O
limited	O
amount	O
of	O
possible	O
16-bit	O
bitmask	O
values	O
in	O
the	O
bit	B-Data_Structure
vector	I-Data_Structure
,	O
678	O
.	O
</s>
<s>
The	O
maptable	O
is	O
constant	O
for	O
any	O
routing	B-Protocol
table	I-Protocol
contents	O
.	O
</s>
<s>
To	O
look	O
up	O
the	O
datum	O
for	O
a	O
given	O
address	B-Protocol
x	O
in	O
the	O
first	O
level	O
of	O
the	O
data	O
structure	O
,	O
the	O
Luleå	B-Protocol
algorithm	I-Protocol
computes	O
three	O
values	O
:	O
</s>
<s>
The	O
second	O
and	O
third	O
levels	O
of	O
the	O
data	O
structure	O
are	O
structured	O
similarly	O
to	O
each	O
other	O
;	O
in	O
each	O
of	O
these	O
levels	O
the	O
Luleå	B-Protocol
algorithm	I-Protocol
must	O
perform	O
prefix	O
matching	O
on	O
8-bit	O
quantities	O
(	O
bits	O
17	O
–	O
24	O
and	O
25	O
–	O
32	O
of	O
the	O
address	B-Protocol
,	O
respectively	O
)	O
.	O
</s>
<s>
The	O
data	O
structure	O
is	O
structured	O
in	O
"	O
chunks	O
"	O
,	O
each	O
of	O
which	O
allows	O
performing	O
this	O
prefix	O
matching	O
task	O
on	O
some	O
subsequence	O
of	O
the	O
address	B-Protocol
space	O
;	O
the	O
data	O
items	O
from	O
the	O
first	O
level	O
data	O
structure	O
point	O
to	O
these	O
chunks	O
.	O
</s>
<s>
If	O
there	O
are	O
few	O
enough	O
different	O
pieces	O
of	O
routing	O
information	O
associated	O
with	O
a	O
chunk	O
,	O
the	O
chunk	O
just	O
stores	O
the	O
list	O
of	O
these	O
routes	O
,	O
and	O
searches	O
through	O
them	O
by	O
a	O
single	O
step	O
of	O
binary	O
search	O
followed	O
by	O
a	O
sequential	B-Algorithm
search	I-Algorithm
.	O
</s>
