Introduction to computer networking Distributed Algorithms Class Recitation.

Introduction to Introduction to computer computer

networkingnetworkingDistributed Algorithms Class Distributed Algorithms Class

RecitationRecitation

Ex. 1 - PIF RevisitedEx. 1 - PIF Revisited• Given the PIF algorithm:

Init: l N(l)0; m0; p0Upon receipt of MSGs(l)

N(l)1if m=0 then

p1send MSGs to all lN-{l}

m1if l’ holds N(l’)=1 then

send MSGs to p m0 l’ N(l’)0

• Is it possible that a node i will send messages to all itsneighbors 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=0T=0

node no. 1 node no. 2 node no. 3 node no. 4time link m1 N1(1) N1(2) p1 m2 N2(1) N2(2) N2(3) p2 m3 N3(1) N3(2) N3(3) p3 m4 N4(1) N4(2) p4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

T=3T=3


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 1



T=4T=4


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 14 (2,4) 1 1 1



T=5T=5


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 14 (2,4) 1 1 15 (2,3) 1 1 25 (4,3) 1



T=6T=6


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 14 (2,4) 1 1 15 (2,3) 1 1 25 (4,3) 16 (1,3) 0 1/0 /0 /06 (3,4) 0 /0 1/0



T=7T=7


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 14 (2,4) 1 1 15 (2,3) 1 1 25 (4,3) 16 (1,3) 0 1/0 /0 /06 (3,4) 0 /0 1/07 (4,2) 1



T=8T=8


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 14 (2,4) 1 1 15 (2,3) 1 1 25 (4,3) 16 (1,3) 0 1/0 /0 /06 (3,4) 0 /0 1/07 (4,2) 18 (3,2) 0 /0 1/0 /0



T=11T=11


0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 (1,2) 1 1 14 (2,4) 1 1 15 (2,3) 1 1 25 (4,3) 16 (1,3) 0 1/0 /0 /06 (3,4) 0 /0 1/07 (4,2) 18 (3,2) 0 /0 1/0 /0

11 (3,1) 111 (2,1) 0 1/0 /0 /0



Ex. 2Ex. 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 ClaimsThe 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; m0; p0Upon receipt of MSGs(l)

N(l)1if m=0 then

p1send MSGs to all neighbours m1

The Claims RevisitedThe 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.

Introduction to computer networking Distributed Algorithms Class Recitation.

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node p

source node

pif algorithm

pifd algorithm

algorithm ends

node i

node j

parent p