<s>
A	O
B-heap	B-Application
is	O
a	O
binary	B-Application
heap	I-Application
implemented	O
to	O
keep	O
subtrees	O
in	O
a	O
single	O
page	O
.	O
</s>
<s>
This	O
reduces	O
the	O
number	O
of	O
pages	O
accessed	O
by	O
up	O
to	O
a	O
factor	O
of	O
ten	O
for	O
big	O
heaps	O
when	O
using	O
virtual	B-Architecture
memory	I-Architecture
,	O
compared	O
with	O
the	O
traditional	O
implementation	O
.	O
</s>
<s>
There	O
are	O
other	O
heap	O
variants	O
which	O
are	O
efficient	O
in	O
computers	O
using	O
virtual	B-Architecture
memory	I-Architecture
or	O
caches	B-General_Concept
,	O
such	O
as	O
cache-oblivious	B-Application
algorithms	I-Application
,	O
k-heaps	O
,	O
and	O
van	O
Emde	O
Boas	O
layouts	O
.	O
</s>
<s>
However	O
,	O
because	O
of	O
the	O
way	O
memory	O
is	O
organized	O
on	O
modern	O
computers	O
into	O
pages	O
in	O
virtual	B-Architecture
memory	I-Architecture
,	O
this	O
scheme	O
of	O
laying	O
out	O
the	O
binary	O
tree	O
can	O
be	O
highly	O
ineffective	O
.	O
</s>
<s>
This	O
will	O
increase	O
the	O
number	O
of	O
page	B-General_Concept
misses	I-General_Concept
,	O
which	O
are	O
very	O
expensive	O
.	O
</s>
<s>
The	O
B-heap	B-Application
solves	O
this	O
problem	O
by	O
laying	O
out	O
child	O
nodes	O
in	O
memory	O
in	O
a	O
different	O
way	O
,	O
trying	O
as	O
much	O
as	O
possible	O
to	O
position	O
subtrees	O
within	O
a	O
single	O
page	O
.	O
</s>
<s>
Therefore	O
,	O
as	O
a	O
vertical	O
traversal	O
proceeds	O
,	O
several	O
of	O
the	O
consecutive	O
retrieved	O
nodes	O
will	O
lay	O
in	O
the	O
same	O
page	O
,	O
leading	O
to	O
a	O
low	O
number	O
of	O
page	B-General_Concept
misses	I-General_Concept
.	O
</s>
<s>
In	O
detail	O
,	O
a	O
b-heap	B-Application
can	O
be	O
implemented	O
in	O
the	O
following	O
way	O
.	O
</s>
<s>
The	O
pages	O
themselves	O
can	O
be	O
seen	O
as	O
a	O
m-ary	B-Data_Structure
tree	I-Data_Structure
,	O
and	O
since	O
half	O
of	O
the	O
elements	O
in	O
each	O
page	O
will	O
be	O
leaves	O
(	O
within	O
the	O
page	O
)	O
,	O
the	O
"	O
tree	O
of	O
pages	O
"	O
has	O
a	O
splitting	O
factor	O
of	O
pagesize/2	O
.	O
</s>
<s>
In	O
contrast	O
to	O
the	O
classic	O
array-like	O
layout	O
,	O
the	O
parent	O
function	O
in	O
a	O
B-heap	B-Application
is	O
more	O
complex	O
because	O
the	O
index	O
of	O
a	O
node	O
's	O
parent	O
must	O
be	O
computed	O
differently	O
depending	O
on	O
where	O
in	O
the	O
page	O
it	O
is	O
.	O
</s>
