Least Cost Rumor Blocking in Social Networks

1. Lecture 7-1 Rumor Blocking Ding-Zhu Du │ UniversityofTexasatDallas│

2. Least Cost Rumor Blocking in Social networks Lidan Fan, Zaixin Lu, Weili Wu, Bhavani Thuraisingham, Huan Ma, Yuanjun Bi. Published in ICDCS2013

3. Outline Background Motivation Problem formulation Related Works Our Contribution Two influence diffusion models Least cost rumor blocking problem Conclusions Future Works

4. Outline Background Motivation Problem formulation Related Works Our Contribution Two influence diffusion models Least cost rumor blocking problem Conclusions Future Works

5. Social networks

6. Social Network Social network is a social structure made up of individuals and relations between these individuals Social network provides a platform for influence diffusion

7. Applications Single cascade • Viral marketing • Recommender systems • Feed ranking • …… Multiple cascades • Political election • Multiple products promotion • Rumor/misinformation controlling • ……

8. Social network properties • Small-world effect The average distance between vertices in a network is short. • Power-law or exponential form There are many nodes with low degree and a small number with high degree. • Clustering or network transitivity Two vertices that are both neighbors of the same third vertex have a high probability of also being neighbors of one another. • Community structure The connections within the same community are dense and between communities are sparse.

9. Influence spreads fast within the same community. • Influence spreads slow across different communities.

11. When misinformation or rumor spreads in social networks, what will happen?

12. A misinformation said that the president of Syria is dead, and it hit the twitter greatly and was circulated fast among the population, leading to a sharp, quick increase in the price of oil. http://news.yahoo.com/blogs/technology-blog/twitter-rumor-leads-sharp-increase-price-oil-173027289.html

13. In August, 2012, thousands of people in Ghazni province left their houses in the middle of the night in panic after the rumor of earthquake. http://www.pajhwok.com/en/2012/08/20/quake-rumour-sends-thousands-ghazni-streets

14. Control the spread of rumors

15. Outline Background Motivation Problem formulation Related Works Our Contribution Two influence diffusion models Least cost rumor blocking problem Conclusions Future Works

16. Rumors generated in a community will influence the members in the network. • Find protectors to reduce the influence of rumors. • Real-world limitation: the overhead spent on protectors and protected members should be balanced. • Rumors spread very fast within their community---too much cost • Rumors spread slow across different communities---little cost • Find least number of protectors to reduce rumor influence to the members in other communities.

17. Our Tasks • Determine influence diffusion models. • Design efficient algorithms to find protectors. • Obtain real world data to evaluate our algorithms.

18. Outline Background Motivation Problem formulation Related Works Our Contribution Two influence diffusion models Least cost rumor blocking problem Conclusions Future Works

20. Outline Background Motivation Problem formulation Related Works Our Contribution Two influence diffusion models Least cost rumor blocking problem Conclusions Future Works

21. Deterministic One Activate Many (DOAM) Opportunistic OneActivateOne (OPOAO)

22. Common properties • Two cascades: rumor and protector; • Diffusion starts time: the same; • Tie breaking rule: protector has priority over rumor; • Status of each node: inactive, infected, protected; • Monotonicity assumption: the status of infected or protected never changes.

23. Deterministic One Activate Many (DOAM)

24. Additional properties of the DOAM model • When a node becomes active (infected or protected), it has a single chance to activate all of its currently inactive (not infected and not protected) neighbors. • The activation attempts succeed with a probability 1.

25. Example 6 2 1 5 3 4 1 is a rumor, 6 is a protector. Step 1: 1--2,3; 6--2,4. 2 and 4 are protected, 3 is infected.

26. Example 6 2 1 5 3 4 Step 2: 4--5. 5 is protected.

27. Opportunistic OneActivateOne (OPOAO)

28. Additional properties of the OPOAO model • At each step, each active (infected or protected) node u can only choose one of its neighbors as its target, and each neighbor is chosen with a probability of 1/deg(u). • Each active (infected or protected) node has unlimited chance to select the same node as its target.

29. 6 2 1 5 3 4 1 is a rumor, 6 is a protector. Step 1:1--2, 6--2. 2 is protected. Example

30. Example 6 2 1 5 3 4 Step 2:1--3, 6--2. 3 is infected.

31. Example 6 2 1 5 3 4 Step 3:1--2, 3--4, 6--4. 4 is protected.

32. Example 6 2 1 5 3 4 Step 4:1--3, 3--2, 6--4, 4--5. 5 is protected.

33. Outline Background Motivation Problem formulation Related Works Our Contribution Two influence diffusion models Least cost rumor blocking problem Conclusions Future Works

34. C0 Red node is a rumor; Yellow nodes are bridge ends. C2 C1 Least Cost Rumor Blocking Problem (LCRB) Bridge ends: • form a vertex set; • belong to neigborhood communities of rumor community; • each can be reached from the rumors before others in its own community.

35. LCRB-D problem for the DOAM model • Given: • community structure • rumors • rumor community • Goal: Find least number of protectors to protect all of the bridge ends.

36. Set Cover Based Greedy (SCBG) Algorithm Main idea • Convert to set cover problem using Breadth First Search (BFS) method. • Three stages: • construct Rumor Forward Search Trees(RFST)--bridge ends • construct Bridge End Backward Search Trees(BEBST)--protector candidates • construct vertex sets used in set cover problem

37. 7 6 9 5 8 3 10 4 11 2 1 Yellow nodes are bridge ends. 12 14 13 Construct Rumor Forward Search Trees(RFST)

38. 4 The minimal hops: 1 hop between 4 and 5; 2 hops between 4 and 12; 3 hops between 4 and 8. 5,8,12 are the bridge ends. 1 2 5 3 12 8 Rumor 4 Forward Search Tree

39. Construct Bridge End Backward Search Trees (BEBST) 7 6 9 5 8 3 10 4 Blue nodes are protector candidates. 11 2 1 12 14 13

40. Bridge End Backward Search Trees 4 4 3 7 4 11 2 9 2 10 3 5 8 12 • Record the protector candidate sets for each bridge end: 5: {5,7}; 8:{2,3,8,9,10,11}; 12:{2,3,12}

41. Construct vertex sets in set cover problem • Find the bridge ends that each candidate can protect: 2:{8,12}; 3:{8,12} ; 5:{5}; 7:{5}; 8:{8}; 9:{8}; 10:{8};11{8}; 12{12} Apply the Greedy algorithm • choose 2 or 3 , bridge ends 8 and 12 are protected; • choose 5 or 7, bridge end 5 is protected; • the output is {2,5} or {2,7} or {3,5} or {3,7}.

42. Theoretical Results • There is a polynomial time O(ln n)−approximation algorithm for the LCRB-D problem, where n is the number of vertices in the set of bridge ends. • If the LCRB-D problem has an approximation algorithm with ratio k(n) if and only if the set cover problem has an approximation algorithm with ratio k(n).

43. Set-Cover Given a collection C of subsets of a set E, find a minimum subcollection C’ of C such that every element of E appears in a subset in C’ .

44. Example of Submodular Function

45. Greedy Algorithm

46. Analysis

50. Weighted Set Cover Given a collection C of subsets of a set E and a weight function w on C, find a minimum total-weight subcollection C’ of C such that every element of E appears in a subset in C’ .