<s>
The	O
routing	B-Protocol
and	I-Protocol
wavelength	I-Protocol
assignment	I-Protocol
(	O
RWA	O
)	O
problem	O
is	O
an	O
optical	O
networking	O
problem	O
with	O
the	O
goal	O
of	O
maximizing	O
the	O
number	O
of	O
optical	O
connections	O
.	O
</s>
<s>
The	O
RWA	O
problem	O
can	O
be	O
formally	O
defined	O
in	O
an	O
integer	B-Algorithm
linear	I-Algorithm
program	I-Algorithm
(	O
ILP	O
)	O
.	O
</s>
<s>
This	O
proof	O
involves	O
a	O
reduction	O
to	O
the	O
Multi-commodity	B-Algorithm
Flow	I-Algorithm
Problem	I-Algorithm
.	O
</s>
<s>
The	O
first	O
method	O
is	O
solving	O
the	O
routing	B-Protocol
portion	O
first	O
,	O
and	O
then	O
assigning	O
a	O
wavelength	O
second	O
.	O
</s>
<s>
Three	O
types	O
of	O
route	O
selection	O
are	O
Fixed	O
Path	O
Routing	B-Protocol
,	O
Fixed	O
Alternate	O
Routing	B-Protocol
,	O
and	O
Adaptive	O
Routing	B-Protocol
.	O
</s>
<s>
Fixed	O
path	O
routing	B-Protocol
is	O
the	O
simplest	O
approach	O
to	O
finding	O
a	O
lightpath	O
.	O
</s>
<s>
Typically	O
this	O
path	O
is	O
computed	O
ahead	O
of	O
time	O
using	O
a	O
shortest	O
path	O
algorithm	O
,	O
such	O
as	O
Dijkstra	B-Algorithm
's	I-Algorithm
Algorithm	I-Algorithm
.	O
</s>
<s>
The	O
SP-1	O
(	O
Shortest	O
Path	O
,	O
1	O
Probe	O
)	O
algorithm	O
is	O
an	O
example	O
of	O
a	O
Fixed	O
Path	O
Routing	B-Protocol
solution	O
.	O
</s>
<s>
The	O
running	B-General_Concept
time	I-General_Concept
is	O
the	O
cost	O
of	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
:	O
,	O
where	O
is	O
the	O
number	O
of	O
edges	O
and	O
is	O
the	O
number	O
of	O
routers	O
.	O
</s>
<s>
The	O
running	B-General_Concept
time	I-General_Concept
is	O
just	O
a	O
constant	O
if	O
a	O
predetermined	O
path	O
is	O
used	O
.	O
</s>
<s>
This	O
definition	O
of	O
SP-1	O
uses	O
the	O
hop	B-Protocol
count	I-Protocol
as	O
the	O
cost	O
function	O
.	O
</s>
<s>
Fixed	O
alternate	O
routing	B-Protocol
is	O
an	O
extension	O
of	O
fixed	O
path	O
routing	B-Protocol
.	O
</s>
<s>
The	O
SP	O
-	O
(	O
Shortest	O
Path	O
,	O
Probes	O
,	O
)	O
algorithm	O
is	O
an	O
example	O
of	O
Fixed	O
Alternate	O
Routing	B-Protocol
.	O
</s>
<s>
The	O
running	B-General_Concept
time	I-General_Concept
using	O
Yen	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
where	O
is	O
the	O
number	O
of	O
edges	O
,	O
is	O
the	O
number	O
of	O
routers	O
,	O
and	O
is	O
the	O
number	O
of	O
paths	O
.	O
</s>
<s>
The	O
running	B-General_Concept
time	I-General_Concept
is	O
a	O
constant	O
factor	O
if	O
the	O
paths	O
are	O
precomputed	O
.	O
</s>
<s>
The	O
major	O
issue	O
with	O
both	O
fixed	O
path	O
routing	B-Protocol
and	O
fixed	O
alternate	O
routing	B-Protocol
is	O
that	O
neither	O
algorithm	O
takes	O
into	O
account	O
the	O
current	O
state	O
of	O
the	O
network	O
.	O
</s>
<s>
Fixed	O
Path	O
Routing	B-Protocol
and	O
Fixed	O
Alternate	O
Routing	B-Protocol
are	O
both	O
not	O
quality	O
aware	O
.	O
</s>
<s>
Five	O
examples	O
of	O
Adaptive	O
Routing	B-Protocol
are	O
LORA	O
,	O
PABR	O
,	O
IA-BF	O
,	O
IA-FF	O
,	O
and	O
AQoS	O
.	O
</s>
<s>
The	O
lexicographical	O
routing	B-Protocol
algorithm	I-Protocol
(	O
LORA	O
)	O
algorithm	O
was	O
proposed	O
in	O
.	O
</s>
<s>
The	O
optimal	O
value	O
of	O
can	O
be	O
calculated	O
using	O
the	O
well-known	O
hill	B-Algorithm
climbing	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Additional	O
constraints	O
can	O
be	O
added	O
and	O
the	O
process	O
repeated	O
indefinitely	O
using	O
a	O
branch	B-Algorithm
and	I-Algorithm
bound	I-Algorithm
approach	O
.	O
</s>
<s>
The	O
authors	O
study	O
a	O
constrained	O
routing	B-Protocol
and	O
spectrum	O
assignment	O
(	O
RSA	O
)	O
problem	O
,	O
which	O
can	O
be	O
reduced	O
to	O
a	O
constrained	O
RWA	O
problem	O
by	O
requesting	O
one	O
slice	O
.	O
</s>
<s>
In	O
the	O
authors	O
report	O
on	O
the	O
generalized	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
,	O
which	O
can	O
be	O
used	O
to	O
efficiently	O
and	O
optimally	O
solve	O
the	O
RWA	O
,	O
RSA	O
,	O
and	O
the	O
routing	B-Protocol
,	O
modulation	O
,	O
and	O
spectrum	O
assignment	O
(	O
RMSA	O
)	O
problems	O
,	O
without	O
the	O
limit	O
on	O
the	O
path	O
length	O
.	O
</s>
