<s>
Edge	B-Protocol
disjoint	I-Protocol
shortest	I-Protocol
pair	I-Protocol
algorithm	I-Protocol
is	O
an	O
algorithm	O
in	O
computer	B-Architecture
network	I-Architecture
routing	B-Protocol
.	O
</s>
<s>
One	O
algorithm	O
is	O
a	O
slight	O
modification	O
of	O
the	O
traditional	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
and	O
the	O
other	O
called	O
the	O
Breadth-First-Search	O
(	O
BFS	O
)	O
algorithm	O
is	O
a	O
variant	O
of	O
the	O
Moore	O
's	O
algorithm	O
.	O
</s>
<s>
In	O
a	O
nonnegative	O
graph	O
,	O
the	O
modified	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
reduces	O
to	O
the	O
traditional	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
and	O
can	O
therefore	O
be	O
used	O
in	O
Step	O
1	O
of	O
the	O
above	O
algorithm	O
(	O
and	O
similarly	O
,	O
the	O
BFS	O
algorithm	O
)	O
.	O
</s>
<s>
graph	O
of	O
Figure	O
C	O
(	O
this	O
is	O
determined	O
using	O
the	O
modified	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
(	O
or	O
the	O
BFS	O
algorithm	O
)	O
valid	O
for	O
such	O
negative	O
arcs	O
;	O
there	O
are	O
never	O
any	O
negative	O
cycles	O
in	O
such	O
a	O
transformed	O
graph	O
)	O
.	O
</s>
<s>
In	O
a	O
nonnegative	O
graph	O
,	O
the	O
modified	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
functions	O
as	O
the	O
traditional	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
In	O
the	O
transformed	O
graph	O
of	O
the	O
edge	B-Protocol
disjoint	I-Protocol
shortest	I-Protocol
pair	I-Protocol
algorithm	I-Protocol
,	O
which	O
contains	O
negative	O
arcs	O
,	O
a	O
given	O
vertex	O
previously	O
"	O
permanently	O
"	O
labeled	O
in	O
Step	O
2a	O
of	O
the	O
modified	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
may	O
be	O
revisited	O
and	O
relabeled	O
in	O
Step	O
3a	O
,	O
and	O
inserted	O
back	O
in	O
vertex	O
set	O
S	O
(	O
Step	O
3b	O
)	O
.	O
</s>
<s>
Most	O
graphs	O
of	O
practical	O
interest	O
are	O
usually	O
sparse	O
,	O
possessing	O
vertex	O
degrees	O
of	O
O(1 )	O
,	O
in	O
which	O
case	O
the	O
efficiency	O
of	O
the	O
modified	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
applied	O
to	O
the	O
transformed	O
graph	O
becomes	O
O( |V|	O
)	O
(	O
or	O
,	O
equivalently	O
,	O
O( |E|	O
)	O
)	O
.	O
</s>
<s>
The	O
edge-disjoint	O
shortest	O
pair	O
algorithm	O
then	O
becomes	O
comparable	O
in	O
efficiency	O
to	O
the	O
Suurballe	B-Protocol
's	I-Protocol
algorithm	I-Protocol
,	O
which	O
in	O
general	O
is	O
of	O
O( |V|2	O
)	O
due	O
to	O
an	O
extra	O
graph	O
transformation	O
that	O
reweights	O
the	O
graph	O
to	O
avoid	O
negative	O
cost	O
arcs	O
,	O
allowing	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
to	O
be	O
used	O
for	O
both	O
shortest	O
path	O
steps	O
.	O
</s>
<s>
By	O
circumventing	O
this	O
additional	O
graph	O
transformation	O
,	O
and	O
using	O
the	O
modified	O
Dijkstra	B-Algorithm
algorithm	I-Algorithm
instead	O
,	O
Bhandari	O
's	O
approach	O
results	O
in	O
a	O
simplified	O
version	O
of	O
the	O
edge	B-Protocol
disjoint	I-Protocol
shortest	I-Protocol
pair	I-Protocol
algorithm	I-Protocol
without	O
sacrificing	O
much	O
in	O
efficiency	O
at	O
least	O
for	O
sparse	O
graphs	O
.	O
</s>
