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Approximation Algorithms in Computational Social Networks
Weili Wu Ding-Zhu DuUniversity 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.
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Textbooks
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“Prerequisites”
Textbook
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Upcoming Springer Book:Optimal Social Influence
Wen Xu, Weili WuUniversity of Texas at Dallas
Some Lectures are selected from
Outline Social Network Online Social Networks Community StructureRumor Blocking
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Web definition: A network consists of two or more nodes that are linked in order to share resources.
What is a Network?
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What is Social Network? Wikipedia Definition: Social Structure •Nodes: Social actors (individuals or organizations)•Links: Social relations
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Example 1: Friendship Network
• Nodes: all persons in the world• A link exists between two persons if they
know each other.
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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 (1933-1984)
Property of Friendship
• Six Degrees of Separation
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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”。
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Family Friend
Family
Friend
Friend
Supervise
Friend
Roommate
Friend
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Lidong Wu
“The small world networkis 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.
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• Erdős number: is the collaboration distance with mathematician Paul Erdős.
What is your Erdős number?
Erdös number 0 --- 1 personErdös number 1 --- 504 peopleErdös number 2 --- 6593 peopleErdös number 3 --- 33605 peopleErdös number 4 --- 83642 peopleErdös number 5 --- 87760 peopleErdös number 6 --- 40014 peopleErdös number 7 --- 11591 peopleErdös number 8 --- 3146 peopleErdös number 9 --- 819 peopleErdös number 10 --- 244 peopleErdös number 11 --- 68 peopleErdös number 12 --- 23 peopleErdös number 13 --- 5 people
* Two persons are linked if they are coauthors of an article.
Coauthorship Network is a Small World Network
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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
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• 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
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There are about 28,537 commercial flights in the sky in the U.S. on any given day.
Network Construction
colors.different with twoendpoints own two its
with edge directed aby drepresente isflight Each
AA123
AA456
AA789Dallas Chicago
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minutes. 30least at needs connection e.g., rules,
someon basedgraph bipartite a into connected areThey
endpoints. of sets twohave city wouldEach
Network Construction
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Dallas
8am
9am
1pm 1pm
9am
3pm 3pm
8am
Network construction
Dallas
8am
9am
1pm 1pm
9am
3pm 3pm
8am
path.shortest node-to-Node
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Outline Social Network Online Social Networks Community StructureRumor Blocking
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Social Network is online in Internet
• Facebook: friendship• linkedIn: friendship• ResearchGate: coauthorship
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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
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What Are OSN Used For?
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Candidates (left to right) ：Ken Livingstone, Boris Johnson and Brian Paddick.
Political Election for Mayor of London
(2012)
Usage Example
http://www.telegraph.co.uk/technology/news/9239077/Twitter-data-predicts-Boris-Johnson-victory.html
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Prediction of Boris Johnson Victory
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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”.
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Outline Social Network Online Social Networks Community StructureRumor Blocking
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Question 1?
Does Six Degrees of Separation imply six degrees of influence?
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Three Degrees of Influencein friendship network
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Three Degrees of InfluenceIn Book Connected by Nicholas A. Christakis and James H. Fowler.
Three Three Degrees of Influence
• The influence of actions ripples through networks 3 hops (to and from your friends’ friends’ friends).
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I am happy!
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Question 2?How to explain Six Degrees of Separation and Three Degrees of Influence?
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Community
• People in a same community share common interests in
- clothes, music, beliefs, movies, food, etc.
• Influence each other strongly.
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* same color, same community
Community without overlap Community with overlap
Community Structure
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• 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
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In the same community,
• Two nodes may have distance more than three.
Community Structure
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For different communities,
Community Structure
• Two nodes can reach each other by at most six steps.
A
CB
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For two overlapping communities,
Outline Social Network Online Social Networks Community StructureRumor Blocking
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04/19/23 46
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.http://news.yahoo.com/blogs/technology-blog/twitter-rumor-leads-sharp-increase-price-oil-173027289.html
04/19/23 47
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
04/19/23 48
04/19/23 49
• People in a same community share common interests in - clothes, music, beliefs, movies, food, etc.
• Influence each other strongly.
Rumor Blocking Problem
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5
1
34
2
8
9
10
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Yellow nodes are bridge ends.
04/19/23 50
Example
1
3
4
5
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1 is a rumor, 6 is a protector.
Step 1: 1--2,3; 6--2,4. 2 and 4 are protected, 3 is infected.
04/19/23 51
rumor
protector
1
3
5
2
4
6
Step 2: 4--5. 5 is protected.
Example
04/19/23 52
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.
04/19/23 53
Hitting Set Problem
67
5
1
34
2
8
9
10
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Yellow nodes are bridge ends.
04/19/23 54
).( all hitting nodes
ofsubset a find tois problem The . protectingfor protector a of
positions possible of )(set aconstruct , end bridgeeach For
uP
u
uPu
Set Cover Problem
67
5
1
34
2
8
9
10
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13
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Yellow nodes are bridge ends.
04/19/23 55
.ends bridge all covering ),( all ofion subcollect a
find tois problem The .at protector a puttingby protected be
can which ends bridge of )(set aconstruct , nodeeach For
uB
u
uBu
Greedy Algorithm
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covered. ends bridge all means done""
done"" until
covered. asset chosen
in ends bridgemark and ends bridge uncovered of
number maximum thecoversset that pick the
Repeat
References
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549-540 :2013 networks. social
in bockingrumor cost Least , Fan,Lidan 2.
in UTD.on dissertati
Ph.D. data, big andsensor Small Wu,Lidong 1.
ICDCS
et al.
THANK YOU!
