Introduction to computer networking Distributed Algorithms Class Recitation

Ex. 1 - PIF Revisited Given the PIF algorithm: Init:  l N(l)  0; m  0; p  0 Upon receipt of MSG s (l) N(l)  1 if m=0 then p  1 send MSG s to all l  N-{l} m  1 if  l’ holds N(l’)=1 then send MSG s to p m  0  l’ N(l’)  0 Is it possible that a node i will send messages to all its neighbors except its parent, p, before node p has? Is it possible for node i to send a message to its parent p before node j has finished sending messages to its neighbors?

T=0

T=3

T=4

T=5

T=6

T=7

T=8

T=11

Ex. 2 Given the PIFD algorithm, which is similar to the PIF algorithm, albeit with a second (other than the source) unique node D which behaves differently from the other nodes. For each of the following claims, determine whether the claim is true or false:

The Claims All the nodes will receive the message after a finite time period and all will have m=1 eventually. The algorithm ends. i.e. there is a finite time after which no more messages are transferred. The source node knows when the algorithm has finished When the source node finishes the algorithm, the algorithm has ended.

PIFD Algorithm For Node D: Init: Init:  l N(l)  0; m  0; p  0 Upon receipt of MSG s (l) N(l)  1 if m=0 then p  1 send MSG s to all neighbours m  1

The Claims Revisited All the nodes will receive the message after a finite time period and all will have m=1 eventually. The algorithm ends. i.e. there is a finite time after which no more messages are transferred. The source node knows when the algorithm has finished When the source node finishes the algorithm, the algorithm has ended.