1. Detect rumor sources 2019/1/3
Previous works in controlling rumor diffusion assume that rumor sources are known. However, in reality, it is hard to know the accurate rumor sources.
Estimate rumor sources accurately using existing information.
Knowing these sources is very important
to the network administrators in the following essences: (1) it
helps to understand the ultimate goals for the misinformation,
who the misleading information targets to as well as the
potential size of the misinformation spread, and (2) it provides
valuable insights into designing effective strategies for the containment campaign.
2019/1/3

2. Rumor Source Detection: monitor placement
Ding-Zhu Du
Department of Computer Science
University of Texas at Dallas

3. OUTLINE Background: Rumor Source Detection Problem Unique Source
Group Testing Approach

4. When misinformation or rumor spreads in social networks, what will happen?
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5. 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.
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6. 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. 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, which said that a major
earthquake would hit the area until 5 am [3]. Believing
in it, many people from the Ghazni city and some other
districts of the province left their house and spent the
whole night outside. The panic spread by the rumor
was so intense that the people, who were in thousands,
did not dare to return to their houses till morning.
Mirwais, a resident of Ghazni city, talked to a news
agency about this announcement. Later, the imams of
the mosques had started believing in it and according
to the statement made by Mirwais, Then, imams of
mosques also started announcing about the earthquake.
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7. Control the spread of rumors
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8. Motivation Rumors spread through the network
We only see who received rumor but not where they got rumor from
Can we locate the hidden rumor sources?

9. Motivation Rumors spread through the network
We only see who received rumor but not where they got rumor from
Can we locate the hidden rumor sources?

10. Problem Description Given Goal Question Applications
Social network structure
Infection time of monitors
Goal
Select a subset of vertices with minimum cardinality such that the rumor source can be uniquely located.
Question
Which set of vertices should we select?
Applications
Epidemiology: Virus
Social Media: Rumor

11. Related Work Shah and Zaman, 2010, 2011, 2012: Luo and Tay, 2012:
“Rumor Centrality”-single source, Susceptible-Infected (SI) model
Luo and Tay, 2012:
Multiple sources, Susceptible-Infected-Recovered (SIR) model
Zhu and Ying, 2013:
Single source estimation for SIR model
Seo et al., 2012; Karamchandani and Franceschetti, 2013; Luo and Tay, 2013; Zhu and Ying, 2014:
Partial observations

12. OUTLINE Background: Rumor Source Detection Problem Unique Source
Group Testing Approach

13. Methodology for Rumor Source Detection
Definition (Set Resolving Set (SRS)). Node set K ⊆ V is an SRS if any different nodes a,b ∈ V are distinguishable by K.
Two nodes a,b ⊆ V are distinguishable by K if there exist two nodes x, y ∈ K such that
: the time that node x received the rumor from A,

14. Influence Propagation Model
Rumor propagates from the sources to any vertex through shortest paths in the network.
As soon as a vertex receives the information, it sends the information to all its neighbors simultaneously, which takes one time unit.
Thus, the time that a rumor initiated at node u is received by node v is ru(v) = s(u) + d(u, v).
Rumor is initiated at different locations at time t, but t is unknown but uniform.

15. An Example of Set Resolving Set (SRS)
{A,B,C} is a SRS. A E F D B C A B C
r(A)-r(B)
r(A)-r(C)
r(B)-r(C) 1 -1 2 -2 D E F

16. Section 3.3

17. A general result on greedy algorithm
With non-integer potential function
Consider a monotone increasing, submodular function
Consider the following problem:
where
is a nonnegative cost function

18. Greedy Algorithm G

19. Theorem Suppose in Greedy Algorithm G, selected x always satisfies
Then its p.r.
where

20. Corollary (New)

21. Proof

22. Equivalence Relation

23. Potential Function

24. Monotone & Submodular

25. Inequality

26. Inequality

29. Greedy Algorithm G(s)

30. Section 3.3

31. Theorem Suppose in Greedy Algorithm G, selected x always satisfies
Then its p.r.
where

32. Required Condition

33. Required Condition

34. Thank you very much!