Introduction to computer networking

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Introduction to computer networking

• Distributed Algorithms Class Recitation

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Ex. 1 - PIF Revisited

• Given the PIF algorithm
• Init ?l N(l)?0 m?0 p?0
• Upon receipt of MSGs(l)
• N(l)?1
• if m0 then
• p?1
• send MSGs to all l?N-l
• m?1
• if ?l holds N(l)1 then
• send MSGs 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?

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T0
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T3
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T4
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T5
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T6
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T7
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T8
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T11
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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

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The Claims

• All the nodes will receive the message after a
  finite time period and all will have m1
  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.

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PIFD
Algorithm For Node D Init Init ?l N(l)?0
m?0 p?0 Upon receipt of MSGs(l) N(l)?1 if m0
then p?1 send MSGs to all neighbours m?1
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The Claims Revisited

• All the nodes will receive the message after a
  finite time period and all will have m1
  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.