1/54 Rumor Source Detection: monitor placement Ding-Zhu Du Department of Computer Science University of Texas at Dallas

2/54 OUTLINE I.Background: Rumor Source Detection Problem II.Unique Source III.Group Testing Approach

3/54 7/8/ When misinformation or rumor spreads in social networks, what will happen?

4/54 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. leads-sharp-increase-price-oil html 7/8/2016 4

5/54 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. e-rumour-sends-thousands-ghazni-streets 7/8/2016 5

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7/54 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?

8/54 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?

9/54 Problem Description Given –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

10/54 Related Work Shah and Zaman, 2010, 2011, 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

11/54 OUTLINE I.Background: Rumor Source Detection Problem II.Unique Source III.Group Testing Approach

12/54 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,

13/54 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 r u (v) = s(u) + d(u, v).

14/54 An Example of Set Resolving Set (SRS) A EF D B C { A,B,C } is a SRS. ABC r(A)-r(B)r(A)-r(C)r(B)-r(C) A011 0 B C12012 D E F21210

15/54 Section

16/54 A general result on greedy algorithm With non-integer potential function Consider a monotone increasing, submodular function Consider the following problem: whereis a nonnegative cost function

17/54 Greedy Algorithm G

18/54 Theorem Suppose in Greedy Algorithm G, selected x always satisfies Then its p.r. where

19/54 Corollary (New)

20/54 Proof

21/54 Equivalence Relation

22/54 Potential Function

23/54 Monotone & Submodular

24/54 Inequality

25/54 Inequality

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28/54 Greedy Algorithm G(s)

29/54 Section

30/54 Theorem Suppose in Greedy Algorithm G, selected x always satisfies Then its p.r. where

31/54 Required Condition

32/54 Required Condition

33/54 THANK YOU VERY MUCH!