<s>
Algorithmic	B-Algorithm
topology	I-Algorithm
,	O
or	O
computational	B-Algorithm
topology	I-Algorithm
,	O
is	O
a	O
subfield	O
of	O
topology	B-Architecture
with	O
an	O
overlap	O
with	O
areas	O
of	O
computer	B-General_Concept
science	I-General_Concept
,	O
in	O
particular	O
,	O
computational	O
geometry	O
and	O
computational	O
complexity	O
theory	O
.	O
</s>
<s>
A	O
primary	O
concern	O
of	O
algorithmic	B-Algorithm
topology	I-Algorithm
,	O
as	O
its	O
name	O
suggests	O
,	O
is	O
to	O
develop	O
efficient	O
algorithms	O
for	O
solving	O
problems	O
that	O
arise	O
naturally	O
in	O
fields	O
such	O
as	O
computational	O
geometry	O
,	O
graphics	O
,	O
robotics	O
,	O
structural	O
biology	O
and	O
chemistry	O
,	O
using	O
methods	O
from	O
computable	B-Algorithm
topology	I-Algorithm
.	O
</s>
<s>
Moreover	O
,	O
it	O
is	O
implemented	O
in	O
the	O
software	O
package	O
Regina	B-Application
.	O
</s>
<s>
The	O
connect-sum	O
decomposition	O
of	O
3-manifolds	O
is	O
also	O
implemented	O
in	O
Regina	B-Application
,	O
has	O
exponential	O
run-time	O
and	O
is	O
based	O
on	O
a	O
similar	O
algorithm	O
to	O
the	O
3-sphere	O
recognition	O
algorithm	O
.	O
</s>
<s>
There	O
are	O
some	O
very	O
popular	O
and	O
successful	O
heuristics	O
,	O
such	O
as	O
SnapPea	B-Language
which	O
has	O
much	O
success	O
computing	O
approximate	O
hyperbolic	O
structures	O
on	O
triangulated	O
3-manifolds	O
.	O
</s>
<s>
SnapPea	B-Language
implements	O
an	O
algorithm	O
to	O
convert	O
a	O
planar	O
knot	O
or	O
link	O
diagram	O
into	O
a	O
cusped	O
triangulation	O
.	O
</s>
<s>
Similarly	O
,	O
SnapPea	B-Language
can	O
convert	O
surgery	O
presentations	O
of	O
3-manifolds	O
into	O
triangulations	O
of	O
the	O
presented	O
3-manifold	O
.	O
</s>
<s>
Algorithms	O
to	O
compute	O
persistent	B-Algorithm
homology	I-Algorithm
of	O
filtered	O
complexes	O
,	O
as	O
in	O
the	O
R	O
package	O
.	O
</s>
