🗣️ Multicast

When one node has information that needs to be spread to the rest of the network

• Needs to be reliable, 100% delivery (atomicity)
• Relatively fast

| CONS: O(n) messages from sender → bottleneck because transmission is limited by sender bandwidth

single point of failure at the sender if sender fails → spread stops

doesn’t guarantee atomicity in delivery | PROS: if tree is balanced, load is O(logn) somewhat better atomicity

CONS: intermediary nodes can fail, message won’t propagate to leaves needs spanning tree setup doesn’t scale well: NAK/ACK floods incur O(n) overhead

EX: SRM sends NAKs with exponential backoff to avoid NAK flood RMTP sends ACKs to only designated receives, still floods though | how it works:

infected nodes pick random targets per round and spread message

possible to receive message multiple times, doesn’t matter though

variants: (1) push, (2) pull, (3) hybrid push-pull | | --- | --- | --- |

➡️ Push Gossip

TLDR: Once you are infected, gossip message to x random targets

INFECTION ANALYSIS

• $x = n \text{ uninfected}, y = 1 \text{ infected}$
• $\frac{dx}{dt} = -\beta xy$
  • negative Beta because overtime # uninfected goes down
  • $\beta = \frac{b}{n}$ is the probability that a given uninfected node (out of b options) is picked by infected node
    • denominator is n because we assume full membership
    • note from HW we learned that even with partial membership (k neighbors ~ large enough to ensure connectivity) we still get same Beta
• c and b are small numbers independent of n
  • $y \approx (n+1) - \frac{1}{n^{cb-2}}$
  • substitute 2 for c → run for t = c log(n) rounds
  • substitute 2 for b → pick b targets each round
  • then plug into equation to see that y or number infected will all (n-1) except $\frac{1}{n^2}$ which is an extremely small fraction of the entire network

PROPERTY 1: Low Latency

• within clog(n) rounds

PROPERTY 2: Reliability