Gossip-Based Ad
Hoc Routing
Zygmunt J. Haas, Joseph
Halpern, LiLi
Cornell University
Presented By Charuka Silva
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Contents
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Introduction
Pure Gossip
Optimization of Gossip
Summary
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Ad Hoc Network
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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.
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Flooding and Gossiping
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Flooding
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Every node that receives a packet retransmits the
packet to all of its neighbors.
Many routing messages are propagated
unnecessarily.
Gossip
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Each node forwards a message with some
probability.
Overhead is reduced.
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Gossip – Bimodal Behavior
Let the gossip probability be p. Then, in
sufficiently large nice graphs, there are
fractions θS(p) and θR(p) such that the gossip
quickly dies out in 1 − θS(p) of the executions
and, in almost all of the fraction θS(p) of the
executions where the gossip does not die
out, a fraction θR(p) of the nodes get the
message. Moreover, in many cases of
interest, θR(p) is close to 1.
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Gossip – Bimodal Behavior (cont.)
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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.
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Contents




Introduction
Pure Gossip
Optimization of Gossip
Summary
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GOSSIP1(p)
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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.
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GOSSIP1(p, k)
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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).
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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 welldefined probability θ0S(p) < 1 that the
message reaches infinitely many nodes.
Moreover, the probability θ0F (p) that a node
receives the message and forwards it in an
execution where the message reaches
infinitely many nodes is equal to θ0S (p).
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Cont.
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θ0S(p) = θ0F (p) =def θ0(p)
In an execution where the message does not
die out, the probability that a random node
receives the message is θ0(p)/p.
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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.
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Experiment – Degree of
network
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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.
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Contents




Introduction
Pure Gossip
Optimization of Gossip
Summary
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A two-threshold scheme
Why?
In a random network, a node may have very
few neighbors, thus the probability that none
of the node’s neighbors will propagate the
gossip is high. We hope that nodes with
lower degree can gossip with higher
probability.
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GOSSIP2(p1, k, p2, n)
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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 > p1. Neighbors
of a node with fewer than n neighbors gossip
with probability p2 instead of p1.
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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).
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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.
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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.
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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).
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Contents




Introduction
Pure Gossip
Optimization of Gossip
Summary
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Summary
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Pure Gossip (GOSSIP1).
Optimization of Gossip (GOSSIP2 and
GOSSIP3).
Integrate Gossip with AODV.
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Thank you!
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