<s>
Memory	B-General_Concept
bound	I-General_Concept
refers	O
to	O
a	O
situation	O
in	O
which	O
the	O
time	O
to	O
complete	O
a	O
given	O
computational	O
problem	O
is	O
decided	O
primarily	O
by	O
the	O
amount	O
of	O
free	O
memory	B-General_Concept
required	O
to	O
hold	O
the	O
working	O
data	O
.	O
</s>
<s>
Memory	B-General_Concept
and	O
computation	O
boundaries	O
can	O
sometimes	O
be	O
traded	O
against	O
each	O
other	O
,	O
e.g.	O
</s>
<s>
by	O
saving	O
and	O
reusing	O
preliminary	O
results	O
or	O
using	O
lookup	B-Data_Structure
tables	I-Data_Structure
.	O
</s>
<s>
Memory-bound	B-General_Concept
functions	I-General_Concept
and	O
memory	B-General_Concept
functions	I-General_Concept
are	O
related	O
in	O
that	O
both	O
involve	O
extensive	O
memory	B-General_Concept
access	O
,	O
but	O
a	O
distinction	O
exists	O
between	O
the	O
two	O
.	O
</s>
<s>
Memory	B-General_Concept
functions	I-General_Concept
use	O
a	O
dynamic	B-Algorithm
programming	I-Algorithm
technique	O
called	O
memoization	O
in	O
order	O
to	O
relieve	O
the	O
inefficiency	O
of	O
recursion	O
that	O
might	O
occur	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
the	O
simple	O
idea	O
of	O
calculating	O
and	O
storing	O
solutions	O
to	O
subproblems	B-Algorithm
so	O
that	O
the	O
solutions	O
can	O
be	O
reused	O
later	O
without	O
recalculating	O
the	O
subproblems	B-Algorithm
again	O
.	O
</s>
<s>
The	O
best	O
known	O
example	O
that	O
takes	O
advantage	O
of	O
memoization	O
is	O
an	O
algorithm	O
that	O
computes	O
the	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
.	O
</s>
<s>
The	O
following	O
pseudocode	B-Language
uses	O
recursion	O
and	O
memoization	O
,	O
and	O
runs	O
in	O
linear	O
CPU	B-Device
time	O
:	O
</s>
<s>
Compare	O
the	O
above	O
to	O
an	O
algorithm	O
that	O
uses	O
only	O
recursion	O
,	O
and	O
runs	O
in	O
exponential	O
CPU	B-Device
time	O
:	O
</s>
<s>
The	O
term	O
"	O
memory-bound	B-General_Concept
function	I-General_Concept
"	O
has	O
surfaced	O
only	O
recently	O
and	O
is	O
used	O
principally	O
to	O
describe	O
a	O
function	O
that	O
uses	O
XOR	O
and	O
consists	O
of	O
a	O
series	O
of	O
computations	O
in	O
which	O
each	O
computation	O
depends	O
on	O
the	O
previous	O
computation	O
.	O
</s>
<s>
Whereas	O
memory	B-General_Concept
functions	I-General_Concept
have	O
long	O
been	O
an	O
important	O
actor	O
in	O
improving	O
time	O
complexity	O
,	O
memory-bound	B-General_Concept
functions	I-General_Concept
have	O
seen	O
far	O
fewer	O
applications	O
.	O
</s>
<s>
Recently	O
,	O
however	O
,	O
scientists	O
have	O
proposed	O
a	O
method	O
using	O
memory-bound	B-General_Concept
functions	I-General_Concept
as	O
a	O
means	O
to	O
discourage	O
spammers	O
from	O
abusing	O
resources	O
,	O
which	O
could	O
be	O
a	O
major	O
breakthrough	O
in	O
that	O
area	O
.	O
</s>
<s>
Memory-bound	B-General_Concept
functions	I-General_Concept
might	O
be	O
useful	O
in	O
a	O
proof-of-work	O
system	O
that	O
could	O
deter	O
spam	O
,	O
which	O
has	O
become	O
a	O
problem	O
of	O
epidemic	O
proportions	O
on	O
the	O
Internet	O
.	O
</s>
<s>
In	O
1992	O
,	O
IBM	O
research	O
scientists	O
Cynthia	O
Dwork	O
and	O
Moni	O
Naor	O
published	O
a	O
paper	O
at	O
CRYPTO	O
1992	O
titled	O
Pricing	O
via	O
Processing	O
or	O
Junk	O
Mail	O
,	O
suggesting	O
a	O
possibility	O
of	O
using	O
CPU-bound	O
functions	O
to	O
deter	O
abusers	O
from	O
sending	O
spam	O
.	O
</s>
<s>
Dwork	O
and	O
Naor	O
proposed	O
that	O
spamming	O
might	O
be	O
reduced	O
by	O
injecting	O
an	O
additional	O
cost	O
in	O
the	O
form	O
of	O
an	O
expensive	O
CPU	B-Device
computation	O
:	O
CPU-bound	O
functions	O
would	O
consume	O
CPU	B-Device
resources	O
at	O
the	O
sender	O
's	O
machine	O
for	O
each	O
message	O
,	O
thus	O
preventing	O
huge	O
amounts	O
of	O
spam	O
from	O
being	O
sent	O
in	O
a	O
short	O
period	O
.	O
</s>
<s>
The	O
major	O
problem	O
of	O
using	O
the	O
above	O
scheme	O
is	O
that	O
fast	O
CPUs	B-Device
compute	O
much	O
faster	O
than	O
slow	O
CPUs	B-Device
.	O
</s>
<s>
If	O
a	O
computation	O
takes	O
a	O
few	O
seconds	O
on	O
a	O
new	O
PC	B-Device
,	O
it	O
may	O
take	O
a	O
minute	O
on	O
an	O
old	O
PC	B-Device
,	O
and	O
several	O
minutes	O
on	O
a	O
PDA	B-Application
,	O
which	O
might	O
be	O
a	O
nuisance	O
for	O
users	O
of	O
old	O
PCs	B-Device
,	O
but	O
probably	O
unacceptable	O
for	O
users	O
of	O
PDAs	B-Application
.	O
</s>
<s>
The	O
disparity	O
in	O
client	O
CPU	B-Device
speed	O
constitutes	O
one	O
of	O
the	O
prominent	O
roadblocks	O
to	O
widespread	O
adoption	O
of	O
any	O
scheme	O
based	O
on	O
a	O
CPU-bound	O
function	O
.	O
</s>
<s>
Therefore	O
,	O
researchers	O
are	O
concerned	O
with	O
finding	O
functions	O
that	O
most	O
computer	O
systems	O
will	O
evaluate	O
at	O
about	O
the	O
same	O
speed	O
,	O
so	O
that	O
high-end	O
systems	O
might	O
evaluate	O
these	O
functions	O
somewhat	O
faster	O
than	O
low-end	O
systems	O
(	O
2	O
–	O
10	O
times	O
faster	O
,	O
but	O
not	O
10	O
–	O
100	O
times	O
faster	O
)	O
as	O
CPU	B-Device
disparities	O
might	O
imply	O
.	O
</s>
<s>
The	O
new	O
egalitarian	O
approach	O
is	O
to	O
rely	O
on	O
memory-bound	B-General_Concept
functions	I-General_Concept
.	O
</s>
<s>
As	O
stated	O
before	O
,	O
a	O
memory-bound	B-General_Concept
function	I-General_Concept
is	O
a	O
function	O
whose	O
computation	O
time	O
is	O
dominated	O
by	O
the	O
time	O
spent	O
accessing	O
memory	B-General_Concept
.	O
</s>
<s>
A	O
memory-bound	B-General_Concept
function	I-General_Concept
accesses	O
locations	O
in	O
a	O
large	O
region	O
of	O
memory	B-General_Concept
in	O
an	O
unpredictable	O
way	O
,	O
in	O
such	O
a	O
way	O
that	O
using	O
caches	O
are	O
not	O
effective	O
.	O
</s>
<s>
In	O
recent	O
years	O
,	O
the	O
speed	O
of	O
CPU	B-Device
has	O
grown	O
drastically	O
,	O
but	O
there	O
has	O
been	O
comparatively	O
small	O
progress	O
in	O
developing	O
faster	O
main	O
memory	B-General_Concept
.	O
</s>
<s>
Since	O
the	O
ratios	O
of	O
memory	B-General_Concept
latencies	I-General_Concept
of	O
machines	O
built	O
in	O
the	O
last	O
five	O
years	O
is	O
typically	O
no	O
greater	O
than	O
two	O
,	O
and	O
almost	O
always	O
less	O
than	O
four	O
,	O
the	O
memory-bound	B-General_Concept
function	I-General_Concept
will	O
be	O
egalitarian	O
to	O
most	O
systems	O
for	O
the	O
foreseeable	O
future	O
.	O
</s>
