<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
AF-heap	B-Application
is	O
a	O
type	O
of	O
priority	B-Application
queue	I-Application
for	O
integer	O
data	O
,	O
an	O
extension	O
of	O
the	O
fusion	B-Data_Structure
tree	I-Data_Structure
using	O
an	O
atomic	O
heap	O
proposed	O
by	O
M	O
.	O
L	O
.	O
Fredman	O
and	O
D	O
.	O
E	O
.	O
Willard	O
.	O
</s>
<s>
Using	O
an	O
AF-heap	B-Application
,	O
it	O
is	O
possible	O
to	O
perform	O
insert	O
or	O
decrease-key	O
operations	O
and	O
delete-min	O
operations	O
on	O
machine-integer	O
keys	O
in	O
time	O
.	O
</s>
<s>
This	O
allows	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
to	O
be	O
performed	O
in	O
the	O
same	O
time	O
bound	O
on	O
graphs	O
with	O
edges	O
and	O
vertices	O
,	O
and	O
leads	O
to	O
a	O
linear	O
time	O
algorithm	O
for	O
minimum	O
spanning	O
trees	O
,	O
with	O
the	O
assumption	O
for	O
both	O
problems	O
that	O
the	O
edge	O
weights	O
of	O
the	O
input	O
graph	O
are	O
machine	O
integers	O
in	O
the	O
transdichotomous	O
model	O
.	O
</s>
