<s>
Pointer	B-Operating_System
jumping	I-Operating_System
or	O
path	B-Operating_System
doubling	I-Operating_System
is	O
a	O
design	O
technique	O
for	O
parallel	B-Operating_System
algorithms	I-Operating_System
that	O
operate	O
on	O
pointer	O
structures	O
,	O
such	O
as	O
linked	B-Data_Structure
lists	I-Data_Structure
and	O
directed	O
graphs	O
.	O
</s>
<s>
Pointer	B-Operating_System
jumping	I-Operating_System
allows	O
an	O
algorithm	O
to	O
follow	O
paths	O
with	O
a	O
time	O
complexity	O
that	O
is	O
logarithmic	O
with	O
respect	O
to	O
the	O
length	O
of	O
the	O
longest	O
path	O
.	O
</s>
<s>
The	O
basic	O
operation	O
of	O
pointer	B-Operating_System
jumping	I-Operating_System
is	O
to	O
replace	O
each	O
neighbor	O
in	O
a	O
pointer	O
structure	O
with	O
its	O
neighbor	O
's	O
neighbor	O
.	O
</s>
<s>
In	O
each	O
step	O
of	O
the	O
algorithm	O
,	O
this	O
replacement	O
is	O
done	O
for	O
all	O
nodes	O
in	O
the	O
data	O
structure	O
,	O
which	O
can	O
be	O
done	O
independently	O
in	O
parallel	B-Operating_System
.	O
</s>
<s>
Pointer	B-Operating_System
jumping	I-Operating_System
is	O
best	O
understood	O
by	O
looking	O
at	O
simple	O
examples	O
such	O
as	O
list	B-Operating_System
ranking	I-Operating_System
and	O
root	O
finding	O
.	O
</s>
<s>
One	O
of	O
the	O
simpler	O
tasks	O
that	O
can	O
be	O
solved	O
by	O
a	O
pointer	B-Operating_System
jumping	I-Operating_System
algorithm	O
is	O
the	O
list	B-Operating_System
ranking	I-Operating_System
problem	O
.	O
</s>
<s>
This	O
problem	O
is	O
defined	O
as	O
follows	O
:	O
given	O
a	O
linked	B-Data_Structure
list	I-Data_Structure
of	O
nodes	O
,	O
find	O
the	O
distance	O
(	O
measured	O
in	O
the	O
number	O
of	O
nodes	O
)	O
of	O
each	O
node	O
to	O
the	O
end	O
of	O
the	O
list	O
.	O
</s>
<s>
This	O
problem	O
can	O
easily	O
be	O
solved	O
in	O
linear	O
time	O
on	O
a	O
sequential	O
machine	O
,	O
but	O
a	O
parallel	B-Operating_System
algorithm	I-Operating_System
can	O
do	O
better	O
:	O
given	O
processors	O
,	O
the	O
problem	O
can	O
be	O
solved	O
in	O
logarithmic	O
time	O
,	O
,	O
by	O
the	O
following	O
pointer	B-Operating_System
jumping	I-Operating_System
algorithm	O
:	O
</s>
<s>
Initialize	O
:	O
for	O
each	O
processor/list	O
node	O
,	O
in	O
parallel	B-Operating_System
:	O
</s>
<s>
For	O
each	O
processor/list	O
node	O
,	O
in	O
parallel	B-Operating_System
:	O
</s>
<s>
The	O
pointer	B-Operating_System
jumping	I-Operating_System
occurs	O
in	O
the	O
last	O
line	O
of	O
the	O
algorithm	O
,	O
where	O
each	O
node	O
's	O
pointer	O
is	O
reset	O
to	O
skip	O
the	O
node	O
's	O
direct	O
successor	O
.	O
</s>
<s>
It	O
is	O
assumed	O
,	O
as	O
in	O
common	O
in	O
the	O
PRAM	B-Operating_System
model	O
of	O
computation	O
,	O
that	O
memory	O
access	O
are	O
performed	O
in	O
lock-step	O
,	O
so	O
that	O
each	O
memory	O
fetch	O
is	O
performed	O
before	O
each	O
memory	O
store	O
;	O
otherwise	O
,	O
processors	O
may	O
clobber	O
each	O
other	O
's	O
data	O
,	O
producing	O
inconsistencies	O
.	O
</s>
<s>
The	O
following	O
diagram	O
follows	O
how	O
the	O
parallel	B-Operating_System
list	B-Operating_System
ranking	I-Operating_System
algorithm	O
uses	O
pointer	B-Operating_System
jumping	I-Operating_System
for	O
a	O
linked	B-Data_Structure
list	I-Data_Structure
with	O
11	O
elements	O
.	O
</s>
<s>
The	O
initialization	O
loop	O
takes	O
constant	O
time	O
,	O
because	O
each	O
of	O
the	O
processors	O
performs	O
a	O
constant	O
amount	O
of	O
work	O
,	O
all	O
in	O
parallel	B-Operating_System
.	O
</s>
<s>
Since	O
the	O
pointer	B-Operating_System
jumping	I-Operating_System
in	O
each	O
iteration	O
splits	O
the	O
list	O
into	O
two	O
parts	O
,	O
one	O
consisting	O
of	O
the	O
"	O
odd	O
"	O
elements	O
and	O
one	O
of	O
the	O
"	O
even	O
"	O
elements	O
,	O
the	O
length	O
of	O
the	O
list	O
pointed	O
to	O
by	O
each	O
processor	O
's	O
is	O
halved	O
in	O
each	O
iteration	O
,	O
which	O
can	O
be	O
done	O
at	O
most	O
time	O
before	O
each	O
list	O
has	O
a	O
length	O
of	O
at	O
most	O
one	O
.	O
</s>
<s>
Following	O
a	O
path	O
in	O
a	O
graph	O
is	O
an	O
inherently	O
serial	O
operation	O
,	O
but	O
pointer	B-Operating_System
jumping	I-Operating_System
reduces	O
the	O
total	O
amount	O
of	O
work	O
by	O
following	O
all	O
paths	O
simultaneously	O
and	O
sharing	O
results	O
among	O
dependent	O
operations	O
.	O
</s>
<s>
Pointer	B-Operating_System
jumping	I-Operating_System
iterates	O
and	O
finds	O
a	O
successor	O
—	O
a	O
vertex	O
closer	O
to	O
the	O
tree	O
root	O
—	O
each	O
time	O
.	O
</s>
<s>
The	O
following	O
pseudocode	B-Language
demonstrates	O
the	O
algorithm	O
.	O
</s>
<s>
The	O
following	O
image	O
provides	O
an	O
example	O
of	O
using	O
pointer	B-Operating_System
jumping	I-Operating_System
on	O
a	O
small	O
forest	O
.	O
</s>
<s>
Although	O
the	O
name	O
pointer	B-Operating_System
jumping	I-Operating_System
would	O
come	O
later	O
,	O
JáJá	O
attributes	O
the	O
first	O
uses	O
of	O
the	O
technique	O
in	O
early	O
parallel	B-Operating_System
graph	O
algorithms	O
and	O
list	B-Operating_System
ranking	I-Operating_System
.	O
</s>
<s>
The	O
technique	O
has	O
been	O
described	O
with	O
other	O
names	O
such	O
as	O
shortcutting	O
,	O
but	O
by	O
the	O
1990s	O
textbooks	O
on	O
parallel	B-Operating_System
algorithms	I-Operating_System
consistently	O
used	O
the	O
term	O
pointer	B-Operating_System
jumping	I-Operating_System
.	O
</s>
<s>
Today	O
,	O
pointer	B-Operating_System
jumping	I-Operating_System
is	O
considered	O
a	O
software	O
design	O
pattern	O
for	O
operating	O
on	O
recursive	O
data	O
types	O
in	O
parallel	B-Operating_System
.	O
</s>
<s>
As	O
a	O
technique	O
for	O
following	O
linked	O
paths	O
,	O
graph	O
algorithms	O
are	O
a	O
natural	O
fit	O
for	O
pointer	B-Operating_System
jumping	I-Operating_System
.	O
</s>
<s>
Consequently	O
,	O
several	O
parallel	B-Operating_System
graph	O
algorithms	O
utilizing	O
pointer	B-Operating_System
jumping	I-Operating_System
have	O
been	O
designed	O
.	O
</s>
<s>
However	O
,	O
pointer	B-Operating_System
jumping	I-Operating_System
has	O
also	O
shown	O
to	O
be	O
useful	O
in	O
a	O
variety	O
of	O
other	O
problems	O
including	O
computer	B-Application
vision	I-Application
,	O
image	B-General_Concept
compression	I-General_Concept
,	O
and	O
Bayesian	O
inference	O
.	O
</s>
