Jing (Selena) He and Hisham M. HaddadDepartment of Computer Science, Kennesaw State University

Shouling Ji, Xiaojing Liao, and Raheem BeyahSchool of Electrical and Computer Engineering, Georgia Institute of Technology

IPCCC 2013

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Minimum-sized Positive Influential Node Set Selection for Social Networks:

Considering Both Positive and Negative Influences

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OUTLINEMotivationProblem DefinitionGreedy AlgorithmPerformance EvaluationConclusions

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Motivation• Example & Applications• Related Work• Contributions

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INTRODUCTION

What is a social network? The graph of relationships and interactions within a group of

individuals.

Motivation

SOCIAL NETWORK AND SPREAD OF INFLUENCE Social network plays a fundamental

role as a medium for the spread of INFLUENCE among its members Opinions, ideas, information,

innovation…

Direct Marketing takes the “word-of-mouth” effects to significantly increase profits (facebook, twitter, myspace, …)

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Motivation

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MOTIVATION

• 900 million users, Apr. 2012• the 3rd largest ― “Country” in the world• More visitors than Google

• Action: Update statues, create event

• More than 4 billion images•Action: Add tags, Add favorites

• 2009, 2 billion tweets per quarter• 2010, 4 billion tweets per quarter•Action: Post tweets, Retweet

Social networks already become a bridge to connectour really daily life and the virtual web space

Motivation

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Who are the opinion leaders in a community?

Marketer Alice

EXAMPLE

Find minimum-sized node (user) set in a social network that could positively influence on every node in the network

Motivation

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APPLICATIONS

Smoking intervention program Promote new products Advertising Social recommendation Expert finding …

Motivation

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RELATED WORK

Influence Maximization (IM) Problem [Kempe03]Select k nodes, maximize the expected number

of influenced individuals

Positive Influence Dominating Set (PIDS) [Wang11]Minimum-sized nominating set D, every other

node has at least half of its neighbors in D

Motivation

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OUR CONTRIBUTIONSo Consider both positive and negative influences

o New optimization problem - Minimum-sized Positive Influential Node Set (MPINS)o Minimum-sized node set that could positively influence every

node in the network no less than a threshold θ

o Propose a greedy algorithm to solve MPINS

o Conduct simulations to validate the proposed algorithm

Motivation

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Problem Definition• Network Model• Diffusion Model• Problem Definition

NETWORK MODEL

A social network is represented as an undirected graph Social influence represented by weights on the edges

Positive influence Negative influence

Nodes start either active or inactive An active node may trigger activation of neighboring

nodes based on a pre-defined threshold θ Monotonicity assumption: active nodes never deactivate

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Problem Definition

DIFFUSION MODEL

Positive influence

Negative influence

Ultimate influence

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Problem Definition

MINIMUM-SIZED POSITIVE INFLUENCE NODE SET (MPINS) Given

a social networka threshold θ

GoalThe initially selected active node set denoted

by I could positively influence every other node in the network

, Objective

Minimize the size of I 14

Problem Definition

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Greedy Algorithm• Contribution function• Example• Correctness proof

CONTRIBUTION FUNCTION

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Greedy algorithm

TWO-PHASE ALGORITHM Maximal Independent Set (M)

Greedy algorithm

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Greedy algorithm

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EXAMPLE

Greedy algorithm

CORRECTNESS PROOF

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Greedy algorithm

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Performance Evaluation• Simulation settings• Simulation results

SIMULATION SETTINGS

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Performance Evaluation

Generate random graph

The weighs on edges are randomly generated

For each specific setting, 100 instances are generated. The results are the average values of these 100 instances

SIMULATION RESULTS – SMALL SCALE

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Performance Evaluation

SIMULATION RESULTS – LARGE SCALE

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Performance Evaluation

SIMULATION RESULTS

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Performance Evaluation

CONCLUSIONS We study MPINS selection problem which has useful

commercial applications in social networks.

We propose a greedy algorithm to solve the problem.

We validate the proposed algorithm through simulation on random graphs representing small size and large size networks.

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Conclusions

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Q & A