<s>
A	O
geometric	B-Algorithm
spanner	I-Algorithm
or	O
a	O
-spanner	O
graph	O
or	O
a	O
-spanner	O
was	O
initially	O
introduced	O
as	O
a	O
weighted	O
graph	O
over	O
a	O
set	O
of	O
points	O
as	O
its	O
vertices	O
for	O
which	O
there	O
is	O
a	O
-path	O
between	O
any	O
pair	O
of	O
vertices	O
for	O
a	O
fixed	O
parameter	O
.	O
</s>
<s>
Therefore	O
geometric	B-Algorithm
spanners	I-Algorithm
are	O
graph	O
spanners	O
of	O
complete	O
graphs	O
embedded	B-Algorithm
in	I-Algorithm
the	I-Algorithm
plane	I-Algorithm
with	O
edge	O
weights	O
equal	O
to	O
the	O
distances	O
between	O
the	O
embedded	O
vertices	O
in	O
the	O
corresponding	O
metric	O
.	O
</s>
<s>
Spanners	O
may	O
be	O
used	O
in	O
computational	O
geometry	O
for	O
solving	O
some	O
proximity	B-Algorithm
problems	I-Algorithm
.	O
</s>
<s>
Chew	O
's	O
main	O
result	O
was	O
that	O
for	O
a	O
set	O
of	O
points	O
in	O
the	O
plane	O
there	O
is	O
a	O
triangulation	B-Algorithm
of	O
this	O
pointset	O
such	O
that	O
for	O
any	O
two	O
points	O
there	O
is	O
a	O
path	O
along	O
the	O
edges	O
of	O
the	O
triangulation	B-Algorithm
with	O
length	O
at	O
most	O
the	O
Euclidean	O
distance	O
between	O
the	O
two	O
points	O
.	O
</s>
<s>
The	O
best	O
upper	O
bound	O
known	O
for	O
the	O
Euclidean	O
Delaunay	B-Algorithm
triangulation	I-Algorithm
is	O
that	O
it	O
is	O
a	O
-spanner	O
for	O
its	O
vertices	O
.	O
</s>
