BUTTERFLY NETWORK
CONTENTS
INTRODUCTION
BUTTERFLY NETWORK BUILDING
ADVANTAGES AND DISADVANTAGES
CONCLUSION
INTRODUCTION
The interconnection network plays a major role in ensuring the
complete performance of a multicomputer system. The idea behind
interconnection networks is that when you have a computing task
involving large amounts of data that cannot be efficiently handled by a
single processor, the task is divided into smaller parallel tasks that are
performed simultaneously so that processing time is reduced .There are
different types of interconnection network techniques but this
discussion focuses on butterfly network.
WHAT IS A BUTTERFLY NETWORK
This is a technique used to link multiple computers into a
high
speed
network.
Its
also
called
multi-stage
interconnection network and can be used to connect
different nodes in a multiprocessor system
It is called a butterfly network because of the pattern
created as connections are made.
BUILDING A BUTTERFLY NETWORK
The process of building a butterfly network can be done
using the diagram in the previous slide as an example.
We have that, the number of processors n=8.
Applying the formula n(log2n + 1) to get the number of
switching nodes;
=n(log2n + 1)
=8×(log28+1)=8×(3+1)
=>32 switching nodes.
Each node can be represented as a N (rank, column number)
for any i > 0, a switching node N(I , j) (i-1, m), in which we get
the value of m by inverting the ith location of j. Let us consider
the node(3,1) ;
I=3 and j=1. The value of m is obtained by inverting the ith bit
of 1.
For the ith = the 3rd bit of the binary value of j which is 1.
Therefore, inverting the third bit results in the binary value
which is 000 which is zero in decimal. Hence m=0. As a result
the nodes connected n(i,j), (i-1, j) ,(i-1,j), (i-1,m) = [ (3,1), (2,1),
(3,0)].
Variable
i
Binary
Representation
001
Decimal
Representation
1
m
000
0
ADVANTAGES AND DISADVANTAGES
ADVANTAGES
Butterfly networks have lower diameter than other topologies like a
linear array, ring and 2-D mesh. This means that in butterfly network a
message transmitted from one processor would get to its destination in a
lower number of network hops.
Butterfly networks have higher bisection bandwidth than other
topologies. Implying that in butterfly network, a higher number of links
ought to be broken in order to prevent global communication.
It has a bigger computer range because it connects a larger number of
computers.
DISADVANTAGE
Butterfly networks are more complex and more expensive than
other topologies since the higher number of links required to
sustain the network is higher.
COMPARING TO OTHER NETWORKS
The difference between butterfly
implementation.
and other networks lies within
Butterfly network has a symmetric structure where all processor nodes
between two ranks are equidistant to each other, whereas hypercube is
more suitable for a multi-processor system which demands unequal
distances between its nodes.
 By looking at the number of links required, it may appear that a network
such as hypercube is cheaper and simpler compared to a butterfly
network, but as the number of processor nodes go beyond 16, router
cost and complexity (represented by degree) of butterfly network
becomes lower than hypercube because its degree is independent of the
number of nodes.
CONCLUSION
In conclusion, no single network topology is best for all scenarios.
The decision is made based on factors like the number of
processor nodes in the system, bandwidth-latency requirements,
cost and scalability.