Examples

Broadcasting and Gossiping

Broadcast on ring (Safe and Forward)

Broadcast on mesh (Safe and Forward)

Hypercube

Important properties of the networks:– Small degree,– Small diameter,– Regular recursive structure,– Easy way to embed trees, etc

Hypercube – two nodes connected if they are differ precisely on one bit

Hypercube – two nodes connected if they are differ precisely on one bit

0 1

00 01

10 11

000 001

010 011

100 101

110 111

0000 0001

0010 0011

0100 0101

0110 0111

1000 1001

1010 1011

1100 1101

1110 1111

1000 001

1010 011

1100 1101

1110 1111

0000 0001

0010 0011

0100 0101

0110 0111

Broadcast on hypercube (S&F)

Broadcast on ring (Cut-Through )

Broadcast on mesh (C-T)

Broadcast on binary tree (C-T)

Gossiping

All-to-All Communication

Gossiping on Ring (Store and Forward)

Gossiping on Mesh (Store and Forward)

Gossiping on Hypercube (S&F)

Gossiping on Ring (and Mesh)Cut-Through Routing

Each process sends m(p-1) words of data because it has an m-word packet for every other processor

The average distance that an m word packet travels is

Since there are p processors, each performing the same type of communication, the total traffic on the network is

The total number of communication channels in the network to share this load is p.

21

1

1 p

p

ip

i

pp

pm 2

)1(

2

)1(

2)1(2

)1(2

ppmt

ppm

p

ppm

w

Hence this procedure cannot be improved by using CT routing

Gossiping on Hypercube (CT routing)