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Gossip-Based Ad Hoc Routing

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Many routing messages are propagated unnecessarily. Gossip ... Optimization of Gossip (GOSSIP2 and GOSSIP3). Integrate Gossip with AODV. 25. Thank you! ... – PowerPoint PPT presentation

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Title: 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!
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