<s>
In	O
mathematical	O
optimization	O
,	O
Zadeh	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
(	O
also	O
known	O
as	O
the	O
least-entered	O
rule	O
)	O
is	O
an	O
algorithmic	O
refinement	O
of	O
the	O
simplex	B-Algorithm
method	I-Algorithm
for	O
linear	B-Algorithm
optimization	I-Algorithm
.	O
</s>
<s>
Zadeh	O
offered	O
a	O
reward	O
of	O
$	O
1,000	O
to	O
anyone	O
who	O
can	O
show	O
that	O
the	O
rule	O
admits	O
polynomially	O
many	O
iterations	O
or	O
to	O
prove	O
that	O
there	O
is	O
a	O
family	O
of	O
linear	B-Algorithm
programs	I-Algorithm
on	O
which	O
the	O
pivoting	O
rule	O
requires	O
subexponentially	O
many	O
iterations	O
to	O
find	O
the	O
optimum	O
.	O
</s>
<s>
Zadeh	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
belongs	O
to	O
the	O
family	O
of	O
history-based	O
improvement	O
rules	O
which	O
,	O
during	O
a	O
run	O
of	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
,	O
retain	O
supplementary	O
data	O
in	O
addition	O
to	O
the	O
current	O
basis	O
of	O
the	O
linear	B-Algorithm
program	I-Algorithm
.	O
</s>
<s>
Zadeh	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
has	O
been	O
shown	O
to	O
have	O
at	O
least	O
super-polynomial	O
time	O
complexity	O
in	O
the	O
worse-case	O
by	O
constructing	O
a	O
family	O
of	O
Markov	O
decision	O
processes	O
on	O
which	O
the	O
policy	O
iteration	O
algorithm	O
requires	O
a	O
super-polynomial	O
number	O
of	O
steps	O
.	O
</s>
<s>
Running	O
the	O
simplex	B-Algorithm
algorithm	I-Algorithm
with	O
Zadeh	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
on	O
the	O
induced	O
linear	B-Algorithm
program	I-Algorithm
then	O
yields	O
a	O
super-polynomial	O
lower	O
bound	O
.	O
</s>
<s>
The	O
result	O
was	O
presented	O
at	O
the	O
"	O
Efficiency	O
of	O
the	O
Simplex	B-Algorithm
Method	I-Algorithm
:	O
Quo	O
vadis	O
Hirsch	O
conjecture	O
?	O
"	O
</s>
<s>
Friedmann	O
's	O
original	O
result	O
has	O
since	O
been	O
strengthened	O
by	O
the	O
construction	O
of	O
an	O
exponential	O
instance	O
for	O
Zadeh	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
.	O
</s>
