<s>
The	O
multi-fragment	O
(	O
MF	O
)	O
algorithm	O
is	O
a	O
heuristic	B-Algorithm
or	O
approximation	B-Algorithm
algorithm	I-Algorithm
for	O
the	O
travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
(	O
TSP	O
)	O
(	O
and	O
related	O
problems	O
)	O
.	O
</s>
<s>
The	O
algorithm	O
builds	O
a	O
tour	O
for	O
the	O
traveling	O
salesman	O
one	O
edge	O
at	O
a	O
time	O
and	O
thus	O
maintains	O
multiple	O
tour	O
fragments	O
,	O
each	O
of	O
which	O
is	O
a	O
simple	O
path	O
in	O
the	O
complete	O
graph	B-Application
of	O
cities	O
.	O
</s>
