Approximation Algorithms in Computational Social Networks Weili Wu Ding-Zhu Du University of Texas at Dallas

Goal This course contains advanced topics in design and analysis of approximation algorithms for optimization problems motivated from study of computational social networks. The goal of this course has two folds: (a) Let students learn techniques in design and analysis of approximation algorithms. (b) Lead students to frontier of research in computational social networks. 2

Textbooks 3

“Prerequisites”

Textbook 5

Upcoming Springer Book: Optimal Social Influence Wen Xu, Weili Wu University of Texas at Dallas Some Lectures are selected from

Lecture 1-1 What is a Social Network? Ding-Zhu Du University of Texas at Dallas

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 8

Web definition: A network consists of two or more nodes that are linked in order to share resources. What is a Network? 9

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What is Social Network? Wikipedia Definition: Social Structure Nodes: Social actors (individuals or organizations) Links: Social relations 11

Example 1: Friendship Network Nodes: all persons in the world A link exists between two persons if they know each other. 12

Milgram (1967) The experiment: Random people from Nebraska were to send a letter (via intermediaries) to a stock broker in Boston. Could only send to someone with whom they know. Six links were needed. Stanley Milgram ( ) Property of Friendship Six Degrees of Separation 13

Chinese Observation 八竿子打不着 形容二者之间关系疏远或毫无关联。 “ 竿 ” 也 作 “ 杆 ” 。 14

Family Friend Family Friend Supervise Friend Roommate Friend 15 Lidong Wu

“The small world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps.”

Example 2: Coauthorship Network Nodes: all publication authors A link exists between two authors if they are coauthors in a publication. 17

Erdős number: is the collaboration distance with mathematician Paul Erd ő s. What is your Erdős number? Erdös number person Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people * Two persons are linked if they are coauthors of an article. Coauthorship Network is a Small World Network 18 Distribution in Dec.2010

My Erdős number is 2. 19

Nodes: all cities with an airport. A link exists between two cities if there exists a direct flight between them. Example 3: Flight Map Is a Small World Network 20

Find a cheap ticket between two given cities. It is a shortest path problem in a social network. Need to add connection information to network. Search Cheap Ticket 21 There are about 28,537 commercial flights in the sky in the U.S. on any given day.

Network Construction AA123 AA456 AA789 Dallas Chicago 22

Network Construction 23 Dallas 8am 9am 1pm 9am 3pm 8am

Network construction Dallas 8am 9am 1pm 9am 3pm 8am 24

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 25

Social Network is online in Internet Facebook: friendship linkedIn: friendship ResearchGate: coauthorship 26

Online Social Networks (OSN) Social influence occurs when one's emotions, opinions, or behaviors are affected by others. Although social influence is possible in the workplace, universities, communities, it is most popular online.

Internet provides a platform to record and to develop social networks 28

What Are OSN Used For? 29

Candidates (left to right) ： Ken Livingstone, Boris Johnson and Brian Paddick. Political Election for Mayor of London (2012) Usage Example /technology/news/ /Twitter-data-predicts- Boris-Johnson-victory.html 30

Prediction of Boris Johnson Victory 31

How to Predict? Analysis posts on Facebook and Twitter: “Sentiment Analysis”. Find 7% more positive sentiment towards Mr. Johnson than Mr. Livingstone. Predict 54% of the vote for Mr. Johnson. Google Insights, tracking web trends, Almost five times more searches for “Boris Johnson” than for “Ken Livingstone” via google.co.uk. Of the total number of web searches for both candidates, 60% were for “Boris Johnson”. 32

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 33

Question 1? Does Six Degrees of Separation imply six degrees of influence? 34

Three Degrees of Influence in friendship network 35

Three Degrees of Influence In Book Connected by Nicholas A. Christakis and James H. Fowler. Nicholas A. ChristakisJames H. Fowler

Three Three Degrees of Influence The influence of actions ripples through networks 3 hops (to and from your friends’ friends’ friends). 37

I am happy! 38

Question 2? How to explain Six Degrees of Separation and Three Degrees of Influence? 39

Community People in a same community share common interests in - clothes, music, beliefs, movies, food, etc. Influence each other strongly. 40

* same color, same community Community without overlap Community with overlap Community Structure 41

two nodes can reach each other in three steps. A few of tied key persons: C, D Member A reaches Member B via A-C-D-B Community Structure 42 In the same community,

Two nodes may have distance more than three. Community Structure 43 For different communities,

Community Structure Two nodes can reach each other by at most six steps. A C B 44 For two overlapping communities,

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 45

10/1/ When misinformation or rumor spreads in social networks, what will happen?

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 10/1/201547

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 10/1/201548

10/1/ People in a same community share common interests in - clothes, music, beliefs, movies, food, etc. Influence each other strongly.

Rumor Blocking Problem Yellow nodes are bridge ends. 10/1/201550

Example is a rumor, 6 is a protector. Step 1: 1--2,3; 6--2,4. 2 and 4 are protected, 3 is infected. 10/1/ rumor protector

Step 2: is protected. Example 10/1/201552

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. C0 C2 C1 Red node is a rumor; Yellow nodes are bridge ends. 10/1/201553

Hitting Set Problem Yellow nodes are bridge ends. 10/1/201554

Set Cover Problem Yellow nodes are bridge ends. 10/1/201555

Greedy Algorithm 56

References 57

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