Download - Rumour Spreading in Social Networks
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Rumour Spreading in Social Networks
Alessandro PanconesiDipartimento 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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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 toa random neighbour
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Gossiping Variants
PUSH
PULL
Node with information sends toa random neighbour
Node without information asks a random neighbour
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Gossiping Variants
PUSH
PULL
Node with information sends toa random neighbour
Node without information asks a random neighbour
PUSH-PULL
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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 ispoly-logarithmic
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OUR GOAL
Prove that rumours spread quickly in a
social network
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Problem formulation:
How many rounds will it take Push-Pull to broadcasta message in a social network?
Prove that rumours spread quickly in a
social network
Recall our goal..
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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 [ICALP’09] 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 [ICALP’09] 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 [STOC’11] show optimal Θ(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 [WWW’08] show that real-world networks (seem to) enjoy high conductance (in the order of log -1 N)
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ConductanceS
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ConductanceS
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ConductanceS
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ConductanceS
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ConductanceS
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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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ResultsChierichetti, Lattanzi, P [SODA’10] With high
probability, regardless of the source, push-pull broadcasts the message within
O(log4 N/ 6) many rounds
Chierichetti, Lattanzi, P [STOC’10] Improved to O( -1 log N log2 -1 )
Giakkoupis [STACS’11] Improved to O( -1 log N)
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ResultsChierichetti, Lattanzi, P [SODA’10] With high
probability, regardless of the source, push-pull broadcasts the message within
O(log4 N/ 6) many rounds
Chierichetti, Lattanzi, P [STOC’10] Improved to O( -1 log N log2 -1 )
Giakkoupis [STACS’11] Improved to O( -1 log N)
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ResultsChierichetti, Lattanzi, P [SODA’10] With high
probability, regardless of the source, push-pull broadcasts the message within
O(log4 N/ 6) many rounds
Chierichetti, Lattanzi, P [STOC’10] Improved to O( -1 log N log2 -1 )
Giakkoupis [STACS’11] Improved to O( -1 log N)
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Results
Θ( -1 log N)
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Variationson the theme
Dörr, Fouz, Sauerwald [STOC’11] 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 [STOC’11] 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 [STOC’11] 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 [STOC’11] 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 [STOC’11] 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 [SODA’12] In power law graphs (Chung-Lu)
• With 2 < α < 3 O(loglog N) rounds are sufficient, with high probability, for Push-Pull to reach a (1-ε) fraction of the network, starting from a random source
• If α > 3 then Ω(logN) rounds are necessary, with high probability
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Variationson the theme
Giakkoupis, Sauerwald [STOC’11] For graphs with vertex expansion at least λ Push-Pull takes
• At most O(λ log5/2 N) rounds to reach every node, with high probability
• At least Ω(λ 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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