<s>
The	O
nearest	B-Algorithm
neighbour	I-Algorithm
algorithm	I-Algorithm
was	O
one	O
of	O
the	O
first	O
algorithms	O
used	O
to	O
solve	O
the	O
travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
approximately	O
.	O
</s>
<s>
The	O
nearest	B-Algorithm
neighbour	I-Algorithm
algorithm	I-Algorithm
is	O
easy	O
to	O
implement	O
and	O
executes	O
quickly	O
,	O
but	O
it	O
can	O
sometimes	O
miss	O
shorter	O
routes	O
which	O
are	O
easily	O
noticed	O
with	O
human	O
insight	O
,	O
due	O
to	O
its	O
"	O
greedy	O
"	O
nature	O
.	O
</s>
<s>
To	O
be	O
precise	O
,	O
for	O
every	O
constant	O
r	O
there	O
is	O
an	O
instance	O
of	O
the	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
such	O
that	O
the	O
length	O
of	O
the	O
tour	O
computed	O
by	O
the	O
nearest	B-Algorithm
neighbour	I-Algorithm
algorithm	I-Algorithm
is	O
greater	O
than	O
r	O
times	O
the	O
length	O
of	O
the	O
optimal	O
tour	O
.	O
</s>
<s>
The	O
nearest	B-Algorithm
neighbour	I-Algorithm
algorithm	I-Algorithm
may	O
not	O
find	O
a	O
feasible	O
tour	O
at	O
all	O
,	O
even	O
when	O
one	O
exists	O
.	O
</s>
