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Broadcast
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Use a spanning tree
Root
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synchronous
•It takes the same time at link to send a message•It takes the same time at each node to process the incoming data
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Time complexity:
d levels
n nodes
Message complexity:
)(dO)(nO
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asynchronous
Links and nodes may have different delays
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slowlink
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slowlink
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Actualdelivery
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Time complexity:
d levels
n nodes
Message complexity:
)(dO)(nO
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Convergecast
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synchronous
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Time complexity:
d levels
n nodes
Message complexity:
)(dO)(nO
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asynchronous
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Time complexity:
d levels
n nodes
Message complexity:
)(dO)(nO
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Building a BFS Spanning Tree
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Tree algorithm for node :
Upon receipt of <invitation> messagefrom neighbor node :
If not member of tree:
v
accept invitation by sending <accept> message to ;
u
v (the father)
If member of tree:decline invitation by sending <reject> message to ; v
Send invitations to all neighbors, except v
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synchronous
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A node initiates the BFS process
<invitation><invitation>
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become membersof tree
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<accept><accept>
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<reject>
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<reject>
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Alternative solution
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reject
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Time complexity:
D diameter
n nodes
Message complexity:
)(DO)(mO
m edges
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asynchronous
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slow node
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reject
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reject
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Time complexity:
D diameter
n nodes
Message complexity:
)(DO)(mO
m edges
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The asynchronous algorithm may give deeper trees than the diameter
Example:
Clique graph
Synchronous BFS Asynchronous BFS
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Building a DFS Spanning Tree
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1reject
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reject
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reject
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Time complexity:
n nodes
Message complexity:
)(mO)(mO
m edges 12
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2
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1
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1
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12
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Building a DFS Spanning Treewith no specified root
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881
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881
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881
reject
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881
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881
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881
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root
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Time complexity:
n nodes
Message complexity:
)(mO)( mnO
m edges 12
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2
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1
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1
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1
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12
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2
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1
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881
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root
