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lidong.wu@utdallas

Lecture 5-1 Positive Influence Dominating Set. Ding-Zhu Du Univ of Texas at Dallas. lidong.wu@utdallas.edu. Social Networks. > 1000 million users The 3 rd largest “Country” in the world More visitors than Google. > 780 million users. 2013, users, 40 % yearly increase.

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lidong.wu@utdallas

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  1. Lecture 5-1 Positive Influence Dominating Set • Ding-Zhu Du • Univ of Texas at Dallas lidong.wu@utdallas.edu

  2. Social Networks • >1000 millionusers • The 3rd largest “Country” in the world • More visitors than Google • >780 millionusers • 2013, users, 40% yearly increase 400 million • 2009, 2 billiontweets per quarter • 2010, 4 billiontweets per quarter • 2011, tweets per quarter 25 billion • More than 6billion images • Pinterest, with a traffic higher than Twitter and Google

  3. A Trillion Dollar Opportunity Online Social networks have become a bridge to connect our daily physical life and the virtual web space On2Off Commerce[1] [1] Online to Offline is trillion dollar business http://techcrunch.com/2010/08/07/why-online2offline-commerce-is-a-trillion-dollar-opportunity/

  4. “Love Obama” I hate Obama, the worst president ever I love Obama Obama is fantastic Obama is great! No Obama in 2012! He cannot be the next president! Positive Negative

  5. What is Social Influence? [1] http://en.wikipedia.org/wiki/Social_influence • Social influence occurs when one's opinions, emotions, or behaviors are affected by others, intentionally or unintentionally.[1] • Informational social influence: to accept information from another; • Normative social influence: to conform to the positive expectations of others.

  6. Three Degree of Influence Six degree of separation[1] Three degree of Influence[2] You are able to influence up to over 1,000,000 persons in the world, according to the Dunbar’s number[3]. [1] S. Milgram. The Small World Problem. Psychology Today, 1967, Vol. 2, 60–67 [2] J.H. Fowler and N.A. Christakis. The Dynamic Spread of Happiness in a Large Social Network: Longitudinal Analysis Over 20 Years in the Framingham Heart Study. British Medical Journal 2008; 337: a2338 [3] R. Dunbar. Neocortex size as a constraint on group size in primates. Human Evolution, 1992, 20: 469–493.

  7. Viral Marketing • Viral marketing or word of mouth strategy • exploits the social network values of customers • the most effective marketing strategy • To study the effects of “word of mouth” in the promotion of new products, Domingos and Richardson posed an algorithmic problem in the year 2001.

  8. Illustrative Example :Influence Maximization • A new product is available in the market. Whom to give free samples to maximize the purchase of the product ?

  9. Problem Setting • Given • a market (e.g. a set of individuals) • estimates for influence between individuals • Goal • Minimum budget for initial advertising (e.g. give away free samples of product) in order to occupy the market. • Question • Which set of individuals should we target at? • Application besides product marketing • spread an innovation, ideas, news • detect stories in blogs • analyze Twitter

  10. Product Advertisement

  11. More Companies: Competition

  12. How to Measure Influence?

  13. A Winning Strategy:Positive Influence

  14. Positive Influence is a Special Threshold Model This is not submodular! x B A

  15. Positive-Influence Max x B A

  16. Min Positive-influence Dominating Set • Given a network, • Find a minimum positive-influence dominating set.

  17. Greedy Algorithm

  18. Section 2.4

  19. A General Problem

  20. Greedy Algorithm

  21. A General Theorem Remark:

  22. Xu Zhu, Jieun Yu, Wonjun Lee, Donghyun Kim, Shan Shan, Ding-Zhu Du: New dominating sets in social networks. J. Global Optimization 48(4): 633-642 (2010) • Min Positive Dominating Set is APX-had. • There exist a polynomial-time (1+ln 1.5Δ)-approximation.

  23. Potential Function Lemma 1 Proof 1 2 3

  24. Proof of 1 B v A x

  25. Proof of 2

  26. Proof of 3

  27. Lemma 2(a) Proof

  28. Lemma 2(b) Proof

  29. Greedy Algorithm

  30. A General Theorem Remark:

  31. Theorem Remark:

  32. Thang N. Dinh, Yilin Shen, Dung T. Nguyen, My T. Thai: On the approximability of positive influence dominating set in social networks. J. Comb. Optim. 27(3): 487-503 (2014) Theorem

  33. Open Problem 1

  34. Open Problem 2

  35. Open Problem 3

  36. THANK YOU!

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