<s>
In	O
computer	O
science	O
,	O
Iacono	B-Data_Structure
's	I-Data_Structure
working	I-Data_Structure
set	I-Data_Structure
structure	I-Data_Structure
is	O
a	O
comparison	O
based	O
dictionary	B-Application
.	O
</s>
<s>
To	O
store	O
a	O
dynamic	O
set	O
of	O
elements	O
,	O
this	O
structure	O
consists	O
of	O
a	O
series	O
of	O
Red	O
–	O
black	O
trees	O
,	O
or	O
other	O
Self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
trees	I-Data_Structure
,	O
and	O
a	O
series	O
of	O
deques	B-Application
(	O
Double-ended	B-Application
queues	I-Application
)	O
,	O
where	O
.	O
</s>
<s>
For	O
every	O
,	O
tree	O
and	O
deque	B-Application
share	O
the	O
same	O
contents	O
and	O
pointers	O
are	O
maintained	O
between	O
their	O
corresponding	O
elements	O
.	O
</s>
<s>
Tree	O
and	O
deque	B-Application
consist	O
of	O
the	O
remaining	O
elements	O
,	O
i.e.	O
,	O
their	O
size	O
is	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
number	O
of	O
items	O
in	O
all	O
trees	O
and	O
the	O
number	O
of	O
elements	O
in	O
all	O
deques	B-Application
both	O
add	O
up	O
to	O
.	O
</s>
<s>
Every	O
element	O
that	O
has	O
been	O
inserted	O
in	O
the	O
data	O
structure	O
is	O
stored	O
in	O
exactly	O
one	O
of	O
the	O
trees	O
and	O
its	O
corresponding	O
deque	B-Application
.	O
</s>
<s>
In	O
the	O
deques	B-Application
of	O
this	O
structure	O
,	O
elements	O
are	O
kept	O
in	O
sorted	O
order	O
according	O
to	O
their	O
working	O
set	O
size	O
.	O
</s>
<s>
Formally	O
,	O
element	O
lies	O
after	O
in	O
deque	B-Application
if	O
and	O
only	O
if	O
.	O
</s>
<s>
Moreover	O
,	O
for	O
every	O
,	O
the	O
elements	O
in	O
deque	B-Application
have	O
a	O
smaller	O
working	O
sets	O
than	O
the	O
elements	O
in	O
deque	B-Application
.	O
</s>
<s>
Since	O
that	O
elements	O
in	O
the	O
deques	B-Application
are	O
sorted	O
with	O
respect	O
to	O
their	O
working	O
sets	O
sizes	O
,	O
a	O
shift	O
operation	O
maintains	O
the	O
Working	O
set	O
invariant	O
.	O
</s>
<s>
The	O
search	O
finishes	O
by	O
performing	O
a	O
shift	O
from	O
to	O
which	O
restores	O
the	O
size	O
of	O
every	O
tree	O
and	O
every	O
deque	B-Application
to	O
their	O
size	O
prior	O
to	O
the	O
search	O
operation	O
.	O
</s>
<s>
Splay	B-Data_Structure
trees	I-Data_Structure
are	O
self	O
adjusting	O
search	O
trees	O
introduced	O
by	O
Sleator	O
and	O
Tarjan	O
in	O
1985	O
.	O
</s>
<s>
Using	O
restructuring	O
heuristic	O
,	O
splay	B-Data_Structure
trees	I-Data_Structure
are	O
able	O
to	O
achieve	O
insert	O
and	O
delete	O
operations	O
in	O
amortized	B-General_Concept
time	I-General_Concept
,	O
without	O
storing	O
any	O
balance	O
information	O
at	O
the	O
nodes	O
.	O
</s>
<s>
Moreover	O
,	O
the	O
Working	O
Set	O
Theorem	O
for	O
splay	B-Data_Structure
trees	I-Data_Structure
states	O
that	O
the	O
cost	O
to	O
access	O
an	O
element	O
in	O
a	O
splay	B-Data_Structure
tree	I-Data_Structure
is	O
amortized	B-General_Concept
.	O
</s>
<s>
Therefore	O
,	O
offering	O
an	O
alternative	O
to	O
splay	B-Data_Structure
trees	I-Data_Structure
.	O
</s>
