<s>
The	O
two-tree	B-Operating_System
broadcast	I-Operating_System
(	O
abbreviated	O
2tree-broadcast	O
or	O
23-broadcast	O
)	O
is	O
an	O
algorithm	O
that	O
implements	O
a	O
broadcast	B-Operating_System
communication	O
pattern	O
on	O
a	O
distributed	B-Architecture
system	I-Architecture
using	O
message	B-Architecture
passing	I-Architecture
.	O
</s>
<s>
A	O
broadcast	B-Operating_System
is	O
a	O
commonly	O
used	O
collective	O
operation	O
that	O
sends	O
data	O
from	O
one	O
processor	O
to	O
all	O
other	O
processors	O
.	O
</s>
<s>
The	O
two-tree	B-Operating_System
broadcast	I-Operating_System
communicates	O
concurrently	O
over	O
two	O
binary	O
trees	O
that	O
span	O
all	O
processors	O
.	O
</s>
<s>
The	O
algorithm	O
can	O
also	O
be	O
adapted	O
to	O
perform	O
a	O
reduction	B-Application
or	O
prefix	B-Application
sum	I-Application
.	O
</s>
<s>
A	O
broadcast	B-Operating_System
sends	O
a	O
message	O
from	O
a	O
specified	O
root	O
processor	O
to	O
all	O
other	O
processors	O
.	O
</s>
<s>
Binary	O
tree	O
broadcasting	B-Operating_System
uses	O
a	O
binary	O
tree	O
to	O
model	O
the	O
communication	O
between	O
the	O
processors	O
.	O
</s>
<s>
To	O
broadcast	B-Operating_System
a	O
message	O
,	O
the	O
root	O
sends	O
to	O
its	O
two	O
children	O
(	O
child	O
nodes	O
)	O
.	O
</s>
<s>
The	O
broadcasting	B-Operating_System
process	O
can	O
be	O
pipelined	O
by	O
splitting	O
the	O
message	O
into	O
blocks	O
,	O
which	O
are	O
then	O
broadcast	B-Operating_System
consecutively	O
.	O
</s>
<s>
The	O
idea	O
of	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
is	O
to	O
use	O
two	O
binary	O
trees	O
and	O
and	O
communicate	O
on	O
both	O
concurrently	O
.	O
</s>
<s>
The	O
data	O
that	O
has	O
to	O
be	O
broadcast	B-Operating_System
is	O
split	O
into	O
blocks	O
of	O
equal	O
size	O
.	O
</s>
<s>
Assume	O
that	O
processor	O
wants	O
to	O
broadcast	B-Operating_System
a	O
message	O
.	O
</s>
<s>
Processor	O
sends	O
blocks	O
alternating	O
to	O
the	O
roots	O
of	O
the	O
two	O
trees	O
,	O
so	O
each	O
tree	O
broadcasts	B-Operating_System
one	O
half	O
of	O
the	O
message	O
.	O
</s>
<s>
In	O
a	O
linear	O
pipeline	O
broadcast	B-Operating_System
,	O
the	O
message	O
is	O
split	O
into	O
blocks	O
.	O
</s>
<s>
For	O
large	O
,	O
the	O
startup	O
latency	O
of	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
is	O
faster	O
.	O
</s>
<s>
A	O
binomial	O
tree	O
broadcast	B-Operating_System
communicates	O
along	O
a	O
binomial	O
tree	O
.	O
</s>
<s>
Each	O
process	O
receives	O
the	O
message	O
that	O
is	O
broadcast	B-Operating_System
(	O
the	O
root	O
already	O
has	O
the	O
message	O
)	O
and	O
then	O
sends	O
the	O
message	O
to	O
its	O
children	O
.	O
</s>
<s>
A	O
binomial	O
tree	O
broadcast	B-Operating_System
has	O
only	O
half	O
the	O
startup	O
time	O
of	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
,	O
but	O
a	O
factor	O
of	O
more	O
communication	O
.	O
</s>
<s>
The	O
binomial	O
tree	O
broadcast	B-Operating_System
is	O
faster	O
than	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
for	O
small	O
messages	O
,	O
but	O
slower	O
for	O
large	O
messages	O
.	O
</s>
<s>
A	O
pipelined	O
binary	O
tree	O
broadcast	B-Operating_System
splits	O
the	O
message	O
into	O
blocks	O
and	O
broadcasts	B-Operating_System
the	O
blocks	O
consecutively	O
over	O
a	O
binary	O
tree	O
.	O
</s>
<s>
The	O
pipelined	O
Fibonacci	O
tree	O
broadcast	B-Operating_System
has	O
half	O
the	O
startup	O
latency	O
of	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
,	O
but	O
also	O
only	O
half	O
of	O
the	O
throughput	O
.	O
</s>
<s>
It	O
is	O
faster	O
for	O
small	O
messages	O
,	O
while	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
is	O
faster	O
for	O
large	O
messages	O
.	O
</s>
<s>
In	O
this	O
case	O
the	O
communication	O
is	O
identical	O
to	O
the	O
broadcast	B-Operating_System
,	O
except	O
that	O
the	O
communication	O
direction	O
is	O
reversed	O
.	O
</s>
<s>
The	O
communication	O
time	O
is	O
the	O
same	O
as	O
for	O
the	O
Broadcast	B-Operating_System
and	O
the	O
amount	O
of	O
data	O
reduced	O
per	O
processor	O
is	O
.	O
</s>
<s>
The	O
processors	O
perform	O
a	O
reduction	B-Application
to	O
the	O
root	O
and	O
the	O
processors	O
perform	O
a	O
reduction	B-Application
to	O
the	O
root	O
.	O
</s>
<s>
Using	O
an	O
inorder	O
binary	O
tree	O
,	O
a	O
prefix	B-Application
sum	I-Application
can	O
be	O
computed	O
by	O
first	O
performing	O
an	O
up-phase	O
in	O
which	O
each	O
interior	O
node	O
computes	O
a	O
partial	O
sum	O
for	O
left	O
-	O
and	O
rightmost	O
leaves	O
and	O
,	O
followed	O
by	O
a	O
down-phase	O
in	O
which	O
prefixes	O
of	O
the	O
form	O
are	O
sent	O
down	O
the	O
tree	O
and	O
allow	O
each	O
processor	O
to	O
finish	O
computing	O
its	O
prefix	B-Application
sum	I-Application
.	O
</s>
<s>
The	O
communication	O
in	O
the	O
up-phase	O
is	O
equivalent	O
to	O
a	O
reduction	B-Application
to	O
processor	O
and	O
the	O
communication	O
in	O
the	O
down-phase	O
is	O
equivalent	O
to	O
a	O
broadcast	B-Operating_System
from	O
the	O
processor	O
.	O
</s>
<s>
The	O
total	O
communication	O
time	O
is	O
about	O
twice	O
the	O
communication	O
time	O
of	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
.	O
</s>
<s>
If	O
is	O
a	O
power	O
of	O
two	O
,	O
there	O
is	O
an	O
optimal	O
broadcasting	B-Operating_System
algorithm	O
based	O
on	O
edge	O
disjoint	O
spanning	O
binomial	O
trees	O
(	O
ESBT	O
)	O
in	O
a	O
hypercube	O
.	O
</s>
<s>
The	O
algorithm	O
uses	O
pipelining	O
by	O
splitting	O
the	O
broadcast	B-Operating_System
data	O
into	O
blocks	O
.	O
</s>
<s>
Processor	O
cyclically	O
distributes	O
blocks	O
to	O
the	O
roots	O
of	O
the	O
ESBTs	O
and	O
each	O
ESBT	O
performs	O
a	O
pipelined	O
binary	O
tree	O
broadcast	B-Operating_System
.	O
</s>
<s>
The	O
communication	O
time	O
of	O
the	O
algorithm	O
is	O
,	O
so	O
the	O
startup	O
latency	O
is	O
only	O
one	O
half	O
of	O
the	O
startup	O
latency	O
of	O
the	O
two-tree	B-Operating_System
broadcast	I-Operating_System
.	O
</s>
<s>
The	O
drawback	O
of	O
the	O
ESBT	O
broadcast	B-Operating_System
is	O
that	O
it	O
does	O
not	O
work	O
for	O
other	O
values	O
of	O
and	O
it	O
cannot	O
be	O
adapted	O
for	O
(	O
non-commutative	O
)	O
reduction	B-Application
or	O
prefix	B-Application
sum	I-Application
.	O
</s>
