1. Multi-Node Broadcasting in Hypercube and Star Graphs
Presenter : Jerry Chen

2. Outline  Introduction  System Model  Multi-Node Broadcasting
 Conclusion

3. Introduction  Broadcast : one-to-all broadcasting
all-to-all broadcasting
multi-node broadcasting (many-to-all)
one-to-all all-to-all many-to-all

4. System Model  Hypercube :
n-dimension, 2n nodes , n2n-1 links , diameter n
Two nodes which differ in exactly one bit .
 Star graph :
n-star, n! nodes , diameter [ 3(n-1)/2 ]
 Assume hypercube and star graph link are full
duplex that can send data in both directions
concurrent .
 The network is synchronous and all nodes are
share a same physical clock .

5. System Model  In-tree :
Root node outdegree=0 and other node outdegree=1
Every edge is pointing, directly or indirectly toward
the root node.
 Out-tree is reverse edge direction by in-tree .
In-tree
Out-tree

6. Multi-Node Broadcasting
 Lemma : In an n-cube, there exist n edge-disjoint
out-tree each located at distinct root and height of n
000
000
000
Three edge-disjoint spanning out-trees

7. Multi-Node Broadcasting
 Lemma : In an n-star, there exist n-1 edge-disjoint
out-trees each located at a distinct root. B B
Four-star edge-disjoint spanning out-tree.

8. A A B C D

9. Broadcasting Algorithm
Unknown number of s source nodes.
Broadcasting message size m bytes
Partition message into t sub-messages
In hypercube t=n , in star graph t=n-1 (in/out-trees)
There are st sub-messages in system
Each source node send its t sub-messages through
one of t in-tree and toward the correspond root.
When the root have collected s sub-messages , then
simultaneously start broadcasting s sub-messages
through the out-tree to all other node.

10. Multi-Node Broadcasting Algorithm
 Two types of packet
1. Data packet ( carry broadcast message )
2. MARKER packet ( control purpose )
# p is a parameter for optimization purpose and time-
slotted into length of Ts+ m/tpTc
 Step 1:
Source node partition message into tp packets and
each contain m/tp bytes. At first slot, the source node
inject packet into t in-tree. And internal node forward
it until root is reached.

11.  Step 2:
1. If terminal node is not a source node then it send
MARKER packet into in-tree in first time slot.
2. If terminal node is also a source node then it will
send MARKER packet in (p+1)-th time slot
# After send out of its own data packets
3. Non-terminal node should forward packets to its
parent and stop at all MARKER packets reach
to root.

12.  Step 3 :
1. After root node has received MARKER packets
from each of its children, it calculate the number
of it received ( must be sp )
2. When it sure received all packets, then root will
start to broadcast all sp data packets to out-tree.
3. All nodes should make a copy of these packets
and further forward to them children.

13.  Conclusion The paper support a efficient algorithm to
broadcast message in hypercube and star graph
architecture.