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ETH Zurich – Distributed Computing – disco.ethz.ch

Convergence in (Social) Influence Networks. Silvio Frischknecht, Barbara Keller, Roger Wattenhofer. ETH Zurich – Distributed Computing – www.disco.ethz.ch. Simple World. 2 Opinions : Opinion changes : Whatever the majority of my friends think. b. b. b. b. b. What Can Happen?.

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ETH Zurich – Distributed Computing – disco.ethz.ch

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  1. Convergence in (Social) Influence Networks Silvio Frischknecht, Barbara Keller, Roger Wattenhofer ETH Zurich – Distributed Computing – www.disco.ethz.ch

  2. Simple World 2 Opinions: Opinion changes: Whateverthemajorityofmyfriendsthink

  3. b

  4. b

  5. b

  6. b

  7. b

  8. What Can Happen? and/or GolesandOlivios 1980

  9. Easy LowerBound: Ω(n)

  10. Easy LowerBound: Ω(n)

  11. Easy LowerBound: Ω(n)

  12. Easy LowerBound: Ω(n)

  13. Easy LowerBound: Ω(n)

  14. UpperBound: v

  15. UpperBound: v

  16. Upper Bound: v

  17. Upper Bound: Goodedge: Friend takesadvisedopinion on nextday Bad edge: Friend does not taketheproposedopinion v

  18. Upper Bound: Goodedge: Friend takesadvisedopinion on nextday Bad edge: Friend does not taketheproposedopinion t t+1 t+2 g g: Nr. ofgoodedges b: Nr. ofbadedges v v b case g > b

  19. Upper Bound: Goodedge: Friend takesadvisedopinion on nextday Bad edge: Friend does not taketheproposedopinion t t+1 t+2 g g: Nr. ofgoodedges b: Nr. ofbadedges v v b case g > b

  20. Upper Bound: Goodedge: Friend takesadvisedopinion on nextday Bad edge: Friend does not taketheproposedopinion t t+1 t+2 g g: Nr. ofgoodedges b: Nr. ofbadedges v v b case g > b

  21. UpperBound: t t+1 t+2 g g: Nr. ofgoodedges b: Nr. ofbadedges v v b case b > g

  22. UpperBound: t t+1 t+2 g g: Nr. ofgoodedges b: Nr. ofbadedges v v b case b > g

  23. UpperBound: t t+1 t+2 g g: Nr. ofgoodedges b: Nr. ofbadedges v v b case b > g

  24. UpperBound: t t+1 t+2 g g g: Nr. ofgoodedges b: Nr. ofbadedges v v b b case b > g

  25. TightBound? LowerboundUpperbound vs.

  26. Let`sVote vs.

  27. Simpler Example:

  28. Simpler Example:

  29. A Transistor

  30. A Transistor

  31. E E B B C C

  32. C C B B E E E E B B C C

  33. C B E E E B B C C

  34. C B C B C B E E E B B B E E E C C C

  35. Other Results Iterative model: Adversarypicksnodesinsteadofsynchronousrounds: 1 Step = 1 nodechangeitsopinion

  36. Convergence Time: θ(n²)

  37. Iterative Model Benevolentalgorithm: θ(n)

  38. תודה רבה

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