Gossip-Based Ad Hoc Routing

1
Gossip-Based Ad Hoc Routing

• Zygmunt J. Haas, Joseph Halpern, LiLi
• Cornell University
• Presented By Charuka Silva

2
Contents

• Introduction
• Pure Gossip
• Optimization of Gossip
• Summary

3
Ad Hoc Network

• Ad Hoc Network is a multi-hop wireless network
  with no fixed infrastructure.
• Robust routing protocols must be developed. Some
  variant of flooding is usually used.

4
Flooding and Gossiping

• Flooding
• Every node that receives a packet retransmits the
  packet to all of its neighbors.
• Many routing messages are propagated
  unnecessarily.
• Gossip
• Each node forwards a message with some
  probability.
• Overhead is reduced.

5
Gossip Bimodal Behavior

• Let the gossip probability be p. Then, in
  sufficiently large nice graphs, there are
  fractions ?S(p) and ?R(p) such that the gossip
  quickly dies out in 1 - ?S(p) of the executions
  and, in almost all of the fraction ?S(p) of the
  executions where the gossip does not die out, a
  fraction ?R(p) of the nodes get the message.
  Moreover, in many cases of interest, ?R(p) is
  close to 1.

6
Gossip Bimodal Behavior (cont.)

• In almost all executions of the algorithm, either
  hardly any nodes receive the message, or most of
  them do.
• By making the fraction of executions where the
  gossip dies out relatively low while also keeping
  the gossip probability low, we can reduce the
  message overhead.

7
Contents

• Introduction
• Pure Gossip
• Optimization of Gossip
• Summary

8
GOSSIP1(p)

• A source sends the route request with probability
  1. When a node first receives a route request,
  with probability p it broadcasts the request to
  its neighbors and with probability 1 p it
  discards the request if the node receives the
  same request again, it is discarded.
• Problem with initial condition of the source
  having very few neighbors.

9
GOSSIP1(p, k)

• For the first k hops, we gossip with probability
  1. From the hop k 1, the gossip probability is
  p.
• GOSSIP1(1, 1) is equivalent to flooding.
• GOSSIP1(p, 1) is equivalent to GOSSIP1(p).

10
Theorem II.1

• For all p 0, for almost all infinite graphs,
  if GOSSIP1(p,0) is used by every node to spread a
  message, then there is a well-defined probability
  ?0S(p) lt 1 that the message reaches infinitely
  many nodes. Moreover, the probability ?0F (p)
  that a node receives the message and forwards it
  in an execution where the message reaches
  infinitely many nodes is equal to ?0S (p).

11
Cont.

• ?0S(p) ?0F (p) def ?0(p)
• In an execution where the message does not die
  out, the probability that a random node receives
  the message is ?0(p)/p.

12
Experiment Probability varies
Gossiping on a random network of average degree
8. The higher the probability, the higher the
fraction of nodes receive the message.
13
Experiment - Probability varies
Gossiping on a random network of average degree
8. The higher the probability, the higher the
fraction of nodes receive the message.
14
Experiment Degree of network

• In a 20 50 regular network of degree 6,
  gossiping with probability .65 ensure that almost
  all nodes get the message in almost all
  executions.
• for a 20 50 regular network of degree 3, we
  need to gossip with probability .86 to ensure
  that almost all nodes get the message in all
  executions.
• Conclusion the higher the degree, the better
  the gossiping effect.

15
GOSSIP1(p, k) - Conclusion

• With p sufficiently high, we can guarantee that
  almost all nodes will receive the message in
  almost all executions.
• Practically, we can guarantee that the
  destination node receives the message, while
  saving a fraction of 1 p of messages.
• The higher the degree, the better the gossiping
  effect

16
Contents

• Introduction
• Pure Gossip
• Optimization of Gossip
• Summary

17
A two-threshold scheme

• Why?
• In a random network, a node may have very few
  neighbors, thus the probability that none of the
  nodes neighbors will propagate the gossip is
  high. We hope that nodes with lower degree can
  gossip with higher probability.

18
GOSSIP2(p1, k, p2, n)

• p1 typical gossip probability.
• k number of hops with which we gossip with
  probability 1.
• n number of neighbors of a node.
• p2 probability for which p2 gt p1. Neighbors of
  a node with fewer than n neighbors gossip with
  probability p2 instead of p1.

19
Comparison of GOSSIP2 with GOSSIP1
GOSSIP2 vs. GOSSIP1 on a random network of
average degree 8 GOSSIP2(0.6,4,1,6) has better
performance than GOSSIP1(0.75,4), while using
4 fewer messages than GOSSIP1(0.75,4).
20
Prevent premature gossip death

• The idea behind
• If a node has n neighbors and the gossip
  probability is p, for each message, the node
  should get roughly pn copies from its neighbors.
  If the node gets significantly fewer than pn
  copies within a reasonable time interval, then
  this is a clue that the message is dying out.

21
GOSSIP3(p, k, m)

• Same as GOSSIP1(p, k) except for the following
  modification
• If a node originally did not broadcast a
  received message, but then did not get the
  message from at least m other nodes within some
  timeout period, then the node will broadcast the
  message immediately after the timeout period.
• Usually m 1.

22
Comparison of GOSSIP3 with GOSSIP1
GOSSIP3 vs. GOSSIP1 on a random network of
average degree 8 GOSSIP3(0.65,4,1) has better
performance than GOSSIP1(0.75,4), while using
8 fewer messages than GOSSIP1(0.75,4).
23
Contents

• Introduction
• Pure Gossip
• Optimization of Gossip
• Summary

24
Summary

• Pure Gossip (GOSSIP1).
• Optimization of Gossip (GOSSIP2 and GOSSIP3).
• Integrate Gossip with AODV.

25
Thank you!