<s>
The	O
KBD	B-Algorithm
algorithm	I-Algorithm
is	O
a	O
cluster	O
update	O
algorithm	O
designed	O
for	O
the	O
fully	O
frustrated	O
Ising	O
model	O
in	O
two	O
dimensions	O
,	O
or	O
more	O
generally	O
any	O
two	O
dimensional	O
spin	O
glass	O
with	O
frustrated	O
plaquettes	O
arranged	O
in	O
a	O
checkered	O
pattern	O
.	O
</s>
<s>
The	O
KBD	B-Algorithm
algorithm	I-Algorithm
is	O
an	O
attempt	O
to	O
extend	O
the	O
bond-formation	O
rule	O
to	O
the	O
plaquettes	O
of	O
the	O
lattice	O
,	O
such	O
that	O
the	O
generated	O
clusters	O
are	O
informed	O
by	O
the	O
frustration	O
profile	O
,	O
resulting	O
in	O
them	O
being	O
smaller	O
than	O
the	O
SW	O
ones	O
,	O
thereby	O
making	O
the	O
algorithm	O
more	O
efficient	O
in	O
comparison	O
.	O
</s>
<s>
It	O
can	O
be	O
shown	O
that	O
the	O
update	O
satisfies	O
detailed	O
balance	O
,	O
meaning	O
that	O
correctness	O
is	O
guaranteed	O
if	O
the	O
algorithm	O
is	O
used	O
in	O
conjunction	O
with	O
ergodic	O
algorithms	O
like	O
single	B-Algorithm
spin-flip	I-Algorithm
updates	I-Algorithm
.	O
</s>
<s>
In	O
this	O
case	O
,	O
on	O
each	O
checkered	O
plaquette	O
,	O
the	O
KBD	B-Algorithm
algorithm	I-Algorithm
will	O
always	O
open	O
two	O
parallel	O
bonds	O
perpendicular	O
to	O
the	O
negative	O
edge	O
,	O
meaning	O
that	O
the	O
bond	O
will	O
be	O
closed	O
on	O
the	O
negative	O
edge	O
along	O
with	O
the	O
edge	O
opposite	O
to	O
it	O
.	O
</s>
<s>
Most	O
importantly	O
,	O
each	O
cycle	O
cannot	O
be	O
contracted	O
to	O
a	O
point	O
in	O
the	O
underlying	O
surface	O
that	O
the	O
lattice	O
is	O
embedded	B-Algorithm
in	O
.	O
</s>
