A ring consists of n nodes. Each node holds a value known only to itself. Design an efficient single-initiator protocol to find the minimum value in a ring. Prove its correctness and analyze its costs.
Note: Each node has 2 neighbors in the ring.
Without lose of generality, lets say we have n nodes from 1....n.
Lets san The ring looks like this 1-2-3.....-n-1
Not that n is linked back to 1 which forms ring, if that edge was not there then there won't be a ring formation by this connection.
Algorithm:
Lets say node 1 is initiator.
Cost-
Each node sends message once so,
we are sending n messages to find minimum value in ring.
Correctness-
Proof that the value find is indeed minimum.
Assume minimum value was m at node i.
So when node i sends value to next node it does
x = min(m,value it got)
since m is minimum so x evaluates to m.
So node i sends m to next node.
Now this m will reach 1 without reducing further as m was the minimum value of a node in ring.
A ring consists of n nodes. Each node holds a value known only to itself. Design...
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