<s>
In	O
computer	B-General_Concept
science	I-General_Concept
a	O
T-tree	B-Data_Structure
is	O
a	O
type	O
of	O
binary	O
tree	B-Application
data	I-Application
structure	I-Application
that	O
is	O
used	O
by	O
main-memory	B-General_Concept
databases	I-General_Concept
,	O
such	O
as	O
Datablitz	B-Application
,	O
eXtremeDB	B-Application
,	O
MySQL	B-Operating_System
Cluster	I-Operating_System
,	O
Oracle	B-Application
TimesTen	I-Application
and	O
MobileLite	O
.	O
</s>
<s>
where	O
both	O
the	O
index	O
and	O
the	O
actual	O
data	O
are	O
fully	O
kept	O
in	O
memory	O
,	O
just	O
as	O
a	O
B-tree	B-Architecture
is	O
an	O
index	O
structure	O
optimized	O
for	O
storage	O
on	O
block	O
oriented	O
secondary	O
storage	O
devices	O
like	O
hard	O
disks	O
.	O
</s>
<s>
T-trees	B-Data_Structure
seek	O
to	O
gain	O
the	O
performance	O
benefits	O
of	O
in-memory	B-General_Concept
tree	B-Data_Structure
structures	I-Data_Structure
such	O
as	O
AVL	O
trees	O
while	O
avoiding	O
the	O
large	O
storage	O
space	O
overhead	O
which	O
is	O
common	O
to	O
them	O
.	O
</s>
<s>
T-trees	B-Data_Structure
do	O
not	O
keep	O
copies	O
of	O
the	O
indexed	O
data	O
fields	O
within	O
the	O
index	O
tree	O
nodes	O
themselves	O
.	O
</s>
<s>
The	O
'	O
T	O
 '	O
in	O
T-tree	B-Data_Structure
refers	O
to	O
the	O
shape	O
of	O
the	O
node	O
data	B-General_Concept
structures	I-General_Concept
in	O
the	O
original	O
paper	O
which	O
first	O
described	O
this	O
type	O
of	O
index	O
.	O
</s>
<s>
A	O
T-tree	B-Data_Structure
node	O
usually	O
consists	O
of	O
pointers	O
to	O
the	O
parent	B-Application
node	I-Application
,	O
the	O
left	O
and	O
right	O
child	B-Data_Structure
node	I-Data_Structure
,	O
an	O
ordered	O
array	O
of	O
data	O
pointers	O
and	O
some	O
extra	O
control	O
data	O
.	O
</s>
<s>
Nodes	O
with	O
two	O
subtrees	B-Application
are	O
called	O
internal	O
nodes	O
,	O
nodes	O
without	O
subtrees	B-Application
are	O
called	O
leaf	B-Application
nodes	I-Application
and	O
nodes	O
with	O
only	O
one	O
subtree	B-Application
are	O
named	O
half-leaf	O
nodes	O
.	O
</s>
<s>
For	O
each	O
internal	O
node	O
,	O
leaf	O
or	O
half	O
leaf	B-Application
nodes	I-Application
exist	O
that	O
contain	O
the	O
predecessor	O
of	O
its	O
smallest	O
data	O
value	O
(	O
called	O
the	O
greatest	O
lower	O
bound	O
)	O
and	O
one	O
that	O
contains	O
the	O
successor	O
of	O
its	O
largest	O
data	O
value	O
(	O
called	O
the	O
least	O
upper	O
bound	O
)	O
.	O
</s>
<s>
If	O
the	O
search	O
value	O
is	O
less	O
than	O
the	O
minimum	O
value	O
of	O
the	O
current	O
node	O
then	O
continue	O
search	O
in	O
its	O
left	O
subtree	B-Application
.	O
</s>
<s>
Search	O
fails	O
if	O
there	O
is	O
no	O
left	O
subtree	B-Application
.	O
</s>
<s>
If	O
the	O
search	O
value	O
is	O
greater	O
than	O
the	O
maximum	O
value	O
of	O
the	O
current	O
node	O
then	O
continue	O
search	O
in	O
its	O
right	O
subtree	B-Application
.	O
</s>
<s>
Search	O
fails	O
if	O
there	O
is	O
no	O
right	O
subtree	B-Application
.	O
</s>
<s>
If	O
the	O
value	O
does	O
n't	O
fit	O
anymore	O
then	O
create	O
a	O
new	O
left	O
or	O
right	O
subtree	B-Application
.	O
</s>
<s>
A	O
T-tree	B-Data_Structure
is	O
implemented	O
on	O
top	O
of	O
an	O
underlying	O
self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
Specifically	O
,	O
Lehman	O
and	O
Carey	O
's	O
article	O
describes	O
a	O
T-tree	B-Data_Structure
balanced	B-Data_Structure
like	O
an	O
AVL	O
tree	O
:	O
it	O
becomes	O
out	O
of	O
balance	O
when	O
a	O
node	O
's	O
child	O
trees	O
differ	O
in	O
height	O
by	O
at	O
least	O
two	O
levels	O
.	O
</s>
<s>
If	O
an	O
imbalance	O
is	O
found	O
,	O
one	O
tree	B-Data_Structure
rotation	I-Data_Structure
or	O
pair	O
of	O
rotations	O
is	O
performed	O
,	O
which	O
is	O
guaranteed	O
to	O
balance	O
the	O
whole	O
tree	O
.	O
</s>
<s>
Although	O
T-trees	B-Data_Structure
were	O
once	O
widely	O
used	O
for	O
main-memory	B-General_Concept
databases	I-General_Concept
because	O
of	O
performance	O
benefits	O
,	O
recent	O
trends	O
for	O
very	O
large	O
main-memory	B-General_Concept
databases	I-General_Concept
put	O
more	O
emphasis	O
on	O
provisioning	O
cost	O
.	O
</s>
