convergence in (social) influence networks
TRANSCRIPT
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ETH Zurich – Distributed Computing – www.disco.ethz.ch
Silvio Frischknecht, Barbara Keller, Roger Wattenhofer
Convergence in (Social) Influence Networks
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Simple World
2 Opinions:
Opinion changes: Whatever the majority of
my friends think
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b
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b
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b
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b
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b
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What Can Happen?
and/or
Goles and Olivios 1980
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Easy Lower Bound: Ω(n)
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Easy Lower Bound: Ω(n)
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Easy Lower Bound: Ω(n)
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Easy Lower Bound: Ω(n)
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Easy Lower Bound: Ω(n)
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Upper Bound:
v
)( 2nO
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v
Upper Bound: )( 2nO
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v
Upper Bound: )( 2nO
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Good edge: Friend takes advised opinion on next day
Bad edge: Friend does not take the proposed opinion
v
Upper Bound: )( 2nO
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Good edge: Friend takes advised opinion on next day
Bad edge: Friend does not take the proposed opinion
v
t t+1 t+2
v g
b
g: Nr. of good edges b: Nr. of bad edges
case g > b
Upper Bound: )( 2nO
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Good edge: Friend takes advised opinion on next day
Bad edge: Friend does not take the proposed opinion
v
t t+1 t+2
v g
b
g: Nr. of good edges b: Nr. of bad edges
case g > b
Upper Bound: )( 2nO
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Good edge: Friend takes advised opinion on next day
Bad edge: Friend does not take the proposed opinion
v
t t+1 t+2
v g
b
g: Nr. of good edges b: Nr. of bad edges
case g > b
Upper Bound: )( 2nO
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v
t t+1 t+2
v g
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
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v
t t+1 t+2
v g
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
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v
t t+1 t+2
v g
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
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v
t t+1 t+2
v g
b
case b > g
g: Nr. of good edges b: Nr. of bad edges
Upper Bound: )( 2nO
b
g
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Tight Bound?
Lower bound Upper bound
vs. 2nn
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Let`s Vote
vs. 2nn
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n
n2
2
log
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Simpler Example: nn
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Simpler Example: nn
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A Transistor
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A Transistor
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B
C
E
B
C
E
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B C
E
E
C B
B C
E
B E
C
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B B C
E E
C
B C
E
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B B B E E E
C C C
B E
C B B
C C
E E
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Other Results
Iterative model: Adversary picks nodes instead of synchronous rounds:
1 Step = 1 node change its opinion
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Convergence Time: θ(n²)
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Iterative Model
Benevolent algorithm: θ(n)
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