Rumour Spreading in Social Networks

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Rumour Spreading in Social Networks

• Alessandro Panconesi
• Dipartimento di Informatica
• Joint work with Flavio Chierichetti and Silvio
  Lattanzi

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Rumours spread quickly
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OUR GOAL
Argue in a rigorous way that rumours spread
quickly in a social network
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(No Transcript)
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How to tackle the problem
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How to tackle the problem
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OUR GOAL
Prove that rumours spread quickly in a social
network
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Gossip a very simple model
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Gossiping
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Gossiping
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Gossiping
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Gossiping
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Gossiping
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Gossiping
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Gossiping
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Gossiping Variants
PUSH
Node with information sends to a random neighbour
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Gossiping Variants
PUSH
Node with information sends to a random neighbour
PULL
Node without information asks a random neighbour
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Gossiping Variants
PUSH-PULL
PUSH
Node with information sends to a random neighbour
PULL
Node without information asks a random neighbour
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Motivation

• Technological Rumour spreading algorithms are
  widely used in communication networks which, more
  and more, are likely to exhibit a social
  dimension. This knowledge might be exploited for
  more efficient communication protocols
• Sociological rumour spreading is a basic, simple
  form of a contagion dynamics. By studying it we
  hope to gain some insight into more complex
  diffusion phenomena

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Previous Work
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Different approach

• We are looking for necessary and/or sufficient
  conditions for rumour spreading to be fast in a
  given network

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Push
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Push
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Push
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Push
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Push
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Push
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Pull
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Pull
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Pull
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Pull
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Pull
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Pull
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Both Push and Pull are hopeless
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Therefore, we consider Push-Pull, quite
appropriately in the Age of the Internet
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Push
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Push
Pull
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Push
Pull
Push-Pull
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OUR GOAL
Prove that rumours spread quickly in a social
network
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Time is of the essence
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Gossiping
0
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Gossiping
1
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Gossiping
1
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Gossiping
1
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Gossiping
2
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Gossiping
2
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Gossiping
3
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Time is of the essence
Time rounds
Speed Time is poly-logarithmic
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OUR GOAL
Prove that rumours spread quickly in a social
network
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Recall our goal..
Prove that rumours spread quickly in a social
network
Problem formulation How many rounds will it take
Push-Pull to broadcast a message in a social
network?
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But..what is a social network??
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Argue about a model
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Argue about a model

• Chierichetti, Lattanzi, P ICALP09 Randomized
  broadcast is fast in PA graphs with high
  probability, regardless of the source, push-pull
  broadcasts the message within O(log2N) many
  rounds

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Argue about a model

• Chierichetti, Lattanzi, P ICALP09 Randomized
  broadcast is fast in PA graphs with high
  probability, regardless of the source, push-pull
  broadcasts the message within O(log2N) many
  rounds
• Dörr, Fouz, Sauerwald STOC11 show optimal
  T(logN) bound holds

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Argue about a model

• However, there is no accepted model for social
  networks

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Empiricism to the rescue

• Leskovec et al WWW08 show that real-world
  networks (seem to) enjoy high conductance (in the
  order of log -1 N)

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Conductance
S
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Conductance
S
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Conductance
S
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Conductance
S
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Conductance
S
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Our Goal finally becomes..
Prove that if a network has high conductance then
rumours spread quickly
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Our Goal finally becomes..
Prove that if a network has high conductance then
rumours spread quickly assuming a worst case
source
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Results

• Chierichetti, Lattanzi, P SODA10 With high
  probability, regardless of the source, push-pull
  broadcasts the message within
• O(log4 N/ ?6)
• many rounds
• Chierichetti, Lattanzi, P STOC10 Improved to
  O( ?-1 log N log2 ?-1 )
• Giakkoupis STACS11 Improved to O( ?-1 log N)

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Results

• Chierichetti, Lattanzi, P SODA10 With high
  probability, regardless of the source, push-pull
  broadcasts the message within
• O(log4 N/ ?6)
• many rounds
• Chierichetti, Lattanzi, P STOC10 Improved to
  O( ?-1 log N log2 ?-1 )
• Giakkoupis STACS11 Improved to O( ?-1 log N)

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Results

• Chierichetti, Lattanzi, P SODA10 With high
  probability, regardless of the source, push-pull
  broadcasts the message within
• O(log4 N/ ?6)
• many rounds
• Chierichetti, Lattanzi, P STOC10 Improved to
  O( ?-1 log N log2 ?-1 )
• Giakkoupis STACS11 Improved to O( ?-1 log N)

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Results
T( ?-1 log N)
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Variationson the theme
Dörr, Fouz, Sauerwald STOC11 Time for
Push-Pull in PA graphs becomes O(log N/ loglog N)
if random choice excludes last used neighbour
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Variationson the theme
Dörr, Fouz, Sauerwald STOC11 Time for
Push-Pull in PA graphs becomes O(log N/ loglog N)
if random choice excludes last used neighbour
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Variationson the theme
Dörr, Fouz, Sauerwald STOC11 Time for
Push-Pull in PA graphs becomes O(log N/ loglog N)
if random choice excludes last used neighbour
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Variationson the theme
Dörr, Fouz, Sauerwald STOC11 Time for
Push-Pull in PA graphs becomes O(log N/ loglog N)
if random choice excludes last used neighbour
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Variationson the theme
Dörr, Fouz, Sauerwald STOC11 Time for
Push-Pull in PA graphs becomes O(log N/ loglog N)
if random choice excludes last used neighbour
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Variationson the theme

• Fountoulakis, Panagiotou, Sauerwald SODA12 In
  power law graphs (Chung-Lu)
• With 2 lt a lt 3 O(loglog N) rounds are
  sufficient, with high probability, for Push-Pull
  to reach a (1-e) fraction of the network,
  starting from a random source
• If a gt 3 then O(logN) rounds are necessary, with
  high probability

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Variationson the theme

• Giakkoupis, Sauerwald STOC11 For graphs with
  vertex expansion at least ? Push-Pull takes
• At most O(? log5/2 N) rounds to reach every node,
  with high probability
• At least O(? log2 N) rounds, with positive
  probability

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To summarize

• There is a close connection between conductance
  (and other expansion properties) and rumour
  spreading
• Since social networks enjoy high conductance,
  this by itself ensures that rumours will spread
  fast

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Things to come

• Rumour spreading without the network
• Rumour spreading in evolving graphs

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THANKS