<s>
A	O
Boltzmann	B-Algorithm
sampler	I-Algorithm
is	O
an	O
algorithm	O
intended	O
for	O
random	O
sampling	O
of	O
combinatorial	O
structures	O
.	O
</s>
<s>
If	O
the	O
object	O
size	O
is	O
viewed	O
as	O
its	O
energy	O
,	O
and	O
the	O
argument	O
of	O
the	O
corresponding	O
generating	O
function	O
is	O
interpreted	O
in	O
terms	O
of	O
the	O
temperature	O
of	O
the	O
physical	O
system	O
,	O
then	O
a	O
Boltzmann	B-Algorithm
sampler	I-Algorithm
returns	O
an	O
object	O
from	O
a	O
classical	O
Boltzmann	O
distribution	O
.	O
</s>
<s>
The	O
concept	O
of	O
Boltzmann	B-Algorithm
sampler	I-Algorithm
was	O
proposed	O
by	O
Philippe	O
Duchon	O
,	O
Philippe	O
Flajolet	O
,	O
Guy	O
Louchard	O
and	O
Gilles	O
Schaeffer	O
in	O
2004	O
.	O
</s>
<s>
is	O
complex	B-Language
analytic	I-Language
.	O
</s>
<s>
More	O
generally	O
,	O
if	O
the	O
disjoint	O
union	O
is	O
taken	O
over	O
a	O
finite	O
set	O
,	O
the	O
resulting	O
Boltzmann	B-Algorithm
sampler	I-Algorithm
can	O
be	O
represented	O
using	O
a	O
random	O
choice	O
with	O
probabilities	O
proportional	O
to	O
the	O
values	O
of	O
the	O
generating	O
functions	O
.	O
</s>
<s>
As	O
the	O
first	O
construction	O
of	O
the	O
sequence	O
operator	O
suggests	O
,	O
Boltzmann	B-Algorithm
samplers	I-Algorithm
can	O
be	O
used	O
recursively	O
.	O
</s>
<s>
where	O
each	O
of	O
the	O
expressions	O
involves	O
only	O
disjoint	O
union	O
,	O
cartesian	O
product	O
and	O
sequence	O
operator	O
,	O
then	O
the	O
corresponding	O
Boltzmann	B-Algorithm
sampler	I-Algorithm
is	O
well	O
defined	O
.	O
</s>
<s>
The	O
original	O
Boltzmann	B-Algorithm
samplers	I-Algorithm
described	O
by	O
Philippe	O
Duchon	O
,	O
Philippe	O
Flajolet	O
,	O
Guy	O
Louchard	O
and	O
Gilles	O
Schaeffer	O
only	O
support	O
basic	O
unlabelled	O
operations	O
of	O
disjoint	O
union	O
,	O
cartesian	O
product	O
and	O
sequence	O
,	O
and	O
two	O
additional	O
operations	O
for	O
labelled	O
classes	O
,	O
namely	O
the	O
set	O
and	O
the	O
cycle	O
construction	O
.	O
</s>
<s>
Since	O
then	O
,	O
the	O
scope	O
of	O
combinatorial	O
classes	O
for	O
which	O
a	O
Boltzmann	B-Algorithm
sampler	I-Algorithm
can	O
be	O
constructed	O
,	O
has	O
expanded	O
.	O
</s>
<s>
Boltzmann	B-Algorithm
samplers	I-Algorithm
for	O
these	O
operations	O
have	O
been	O
described	O
by	O
Philippe	O
Flajolet	O
,	O
Éric	O
Fusy	O
and	O
Carine	O
Pivoteau	O
.	O
</s>
<s>
Boltzmann	B-Algorithm
samplers	I-Algorithm
for	O
differential	O
specifications	O
have	O
been	O
constructed	O
by	O
Olivier	O
Bodini	O
,	O
Olivier	O
Roussel	O
and	O
Michèle	O
Soria	O
.	O
</s>
<s>
Each	O
of	O
the	O
size	O
functions	O
can	O
reflect	O
one	O
of	O
the	O
parameters	O
of	O
a	O
data	B-General_Concept
structure	I-General_Concept
,	O
such	O
as	O
the	O
number	O
of	O
leaves	O
of	O
certain	O
colour	O
in	O
a	O
tree	O
,	O
the	O
height	O
of	O
the	O
tree	O
,	O
etc	O
.	O
</s>
<s>
Multiparametric	O
Boltzmann	B-Algorithm
samplers	I-Algorithm
have	O
been	O
constructed	O
by	O
Olivier	O
Bodini	O
and	O
Yann	O
Ponty	O
.	O
</s>
