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

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

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

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 .

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

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

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.

A A B C D

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.

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.

 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.

 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.

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