<s>
In	O
computer	O
science	O
,	O
finger	B-Algorithm
search	I-Algorithm
trees	I-Algorithm
are	O
a	O
type	O
of	O
binary	B-Language
search	I-Language
tree	I-Language
that	O
keeps	O
pointers	O
to	O
interior	O
nodes	O
,	O
called	O
fingers	O
.	O
</s>
<s>
It	O
should	O
not	O
be	O
confused	O
with	O
a	O
finger	B-Application
tree	I-Application
nor	O
a	O
splay	B-Data_Structure
tree	I-Data_Structure
,	O
although	O
both	O
can	O
be	O
used	O
to	O
implement	O
finger	B-Algorithm
search	I-Algorithm
trees	I-Algorithm
.	O
</s>
<s>
introduced	O
finger	B-Algorithm
search	I-Algorithm
trees	I-Algorithm
,	O
by	O
building	O
upon	O
B-trees	B-Architecture
.	O
</s>
<s>
The	O
original	O
version	O
supports	O
finger	B-Algorithm
searches	I-Algorithm
in	O
O(log d )	O
time	O
,	O
where	O
d	O
is	O
the	O
number	O
of	O
elements	O
between	O
the	O
finger	O
and	O
the	O
search	O
target	O
.	O
</s>
<s>
Huddleston	O
and	O
Mehlhorn	O
refined	O
this	O
idea	O
as	O
level-linked	O
B-trees	B-Architecture
.	O
</s>
<s>
To	O
perform	O
a	O
finger	B-Algorithm
search	I-Algorithm
on	O
a	O
binary	O
tree	O
,	O
the	O
ideal	O
way	O
is	O
to	O
start	O
from	O
the	O
finger	O
,	O
and	O
search	O
upwards	O
to	O
the	O
root	O
,	O
until	O
we	O
reach	O
the	O
least	O
common	O
ancestor	O
,	O
also	O
called	O
the	O
turning	O
node	O
,	O
of	O
x	O
and	O
y	O
,	O
and	O
then	O
go	O
downwards	O
to	O
find	O
the	O
element	O
we	O
're	O
looking	O
for	O
.	O
</s>
<s>
Treaps	B-Application
,	O
a	O
randomized	O
tree	O
structure	O
proposed	O
by	O
Seidel	O
and	O
Aragon	O
,	O
has	O
the	O
property	O
that	O
the	O
expected	O
path	O
length	O
of	O
two	O
elements	O
of	O
distance	O
d	O
is	O
O(log d )	O
.	O
</s>
<s>
A	O
book	O
chapter	O
has	O
been	O
written	O
that	O
covers	O
finger	B-Algorithm
search	I-Algorithm
trees	I-Algorithm
in	O
depth	O
.	O
</s>
<s>
In	O
which	O
,	O
Brodal	O
suggested	O
an	O
algorithm	O
to	O
perform	O
finger	B-Algorithm
search	I-Algorithm
on	O
treaps	B-Application
in	O
O(log d )	O
time	O
,	O
without	O
needing	O
any	O
extra	O
bookkeeping	O
information	O
;	O
this	O
algorithm	O
accomplishes	O
this	O
by	O
concurrently	O
searching	O
downward	O
from	O
the	O
last	O
candidate	O
LCA	O
.	O
</s>
