<s>
Prune	B-Algorithm
and	I-Algorithm
search	I-Algorithm
is	O
a	O
method	O
of	O
solving	O
optimization	O
problems	O
suggested	O
by	O
Nimrod	O
Megiddo	O
in	O
1983	O
.	O
</s>
<s>
As	O
such	O
,	O
it	O
is	O
a	O
form	O
of	O
decrease	B-Algorithm
and	I-Algorithm
conquer	I-Algorithm
algorithm	I-Algorithm
,	O
where	O
at	O
each	O
step	O
the	O
decrease	O
is	O
by	O
a	O
constant	O
factor	O
.	O
</s>
<s>
In	O
prune	B-Algorithm
and	I-Algorithm
search	I-Algorithm
algorithms	O
S(n )	O
is	O
typically	O
at	O
least	O
linear	O
(	O
since	O
the	O
whole	O
input	O
must	O
be	O
processed	O
)	O
.	O
</s>
<s>
This	O
can	O
be	O
seen	O
either	O
by	O
applying	O
the	O
master	B-Algorithm
theorem	I-Algorithm
for	I-Algorithm
divide-and-conquer	I-Algorithm
recurrences	I-Algorithm
or	O
by	O
observing	O
that	O
the	O
times	O
for	O
the	O
recursive	O
subproblems	O
decrease	O
in	O
a	O
geometric	O
series	O
.	O
</s>
<s>
In	O
particular	O
,	O
Megiddo	O
himself	O
used	O
this	O
approach	O
in	O
his	O
linear	O
time	O
algorithm	O
for	O
the	O
linear	B-Algorithm
programming	I-Algorithm
problem	I-Algorithm
when	O
the	O
dimension	O
is	O
fixed	O
and	O
for	O
the	O
minimal	B-Algorithm
enclosing	I-Algorithm
sphere	I-Algorithm
problem	O
for	O
a	O
set	O
of	O
points	O
in	O
space	O
.	O
</s>
