<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
2	B-Application
–	I-Application
3	I-Application
heap	I-Application
is	O
a	O
data	B-General_Concept
structure	I-General_Concept
,	O
a	O
variation	O
on	O
the	O
heap	B-Application
,	O
designed	O
by	O
Tadao	O
Takaoka	O
in	O
1999	O
.	O
</s>
<s>
The	O
structure	O
is	O
similar	O
to	O
the	O
Fibonacci	B-Application
heap	I-Application
,	O
and	O
borrows	O
from	O
the	O
2	B-Data_Structure
–	I-Data_Structure
3	I-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
Time	O
costs	O
for	O
some	O
common	O
heap	B-Application
operations	O
are	O
:	O
</s>
<s>
Delete-min	O
takes	O
amortized	B-General_Concept
time	I-General_Concept
.	O
</s>
<s>
Decrease-key	O
takes	O
constant	O
amortized	B-General_Concept
time	I-General_Concept
.	O
</s>
<s>
Insertion	O
takes	O
constant	O
amortized	B-General_Concept
time	I-General_Concept
.	O
</s>
<s>
Furthermore	O
,	O
an	O
r-ary	O
polynomial	O
of	O
trees	O
is	O
called	O
an	O
r-nomial	O
queue	O
if	O
nodes	O
of	O
the	O
polynomial	O
of	O
trees	O
are	O
associated	O
with	O
keys	O
in	O
heap	B-Application
property	I-Application
.	O
</s>
<s>
If	O
we	O
assign	O
keys	O
into	O
the	O
nodes	O
of	O
an	O
extended	O
polynomial	O
of	O
trees	O
in	O
heap	B-Application
order	O
it	O
is	O
called	O
,	O
and	O
the	O
special	O
case	O
of	O
and	O
is	O
called	O
.	O
</s>
<s>
Insertion	O
:	O
In	O
order	O
to	O
insert	O
a	O
new	O
key	O
,	O
we	O
merge	O
the	O
currently	O
existing	O
(	O
2	O
,	O
3	O
)	O
-heap	O
with	O
a	O
single	O
node	O
tree	O
,	O
labeled	O
with	O
this	O
key	O
.	O
</s>
