ETH Zurich – Distributed Computing – www.disco.ethz.ch Barbara Keller, Panda Metaiel Majority Voting: San Rocco or Ulisse?
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ETH Zurich – Distributed Computing – www.disco.ethz.ch
Barbara Keller, Panda Metaiel
Majority Voting: San Rocco or Ulisse?
Simple World
2 Opinions:
Opinion changes: Whatever the majority of my friends think
b
b
b
b
b
What Can Happen?
and/or
Goles and Olivios 1980
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Easy Lower Bound: Ω(n)
Upper Bound?
Winkler 2008
Upper Bound:
v
)( 2nO
v
Upper Bound: )( 2nO
v
Upper Bound: )( 2nO
Good edge: Friend takes advised opinion on next day
Bad edge: Friend does not take the proposed opinion
v
Upper Bound: )( 2nO
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
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
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
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
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
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
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
Upper Bound:
)( 2nO
Winkler 2008
Tight Bound?
Lower bound Upper bound
vs. 2nn
Let`s Vote
vs. 2nn
n
n2
2
log
Simpler Example: nn
Different Models
Yes! No!
2Θ(𝑛) 𝑛2+𝑂(1) 𝑂(𝑛2)
Let`s Vote Again!
Only a Little Bit!
Yes! No!
2Θ(𝑛) 𝑛2+𝑂(1) 𝑂(𝑛2)
Let`s Vote Again!
Only a Little Bit!
Animations
http://www.disco.ethz.ch/members/barkelle/FUN.zip
-9001 9001
No Changes
Exponentially long circles!
San Rocco or Ulisse?
Grazie!
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