MINIMUM-SIZED INFLUENTIAL NODE SET SELECTION FOR SOCIAL NETWORKS UNDER THE INDEPENDENT CASCADE MODEL MobiHoc 2014 Jing (Selena) He Department of Computer Science, Kennesaw State University Shouling Ji, and Raheem Beyah School of Electrical and Computer Engineering, Georgia Institute of Technology Zhipeng Cai Department of Computer Science, Georgia State University
Slide 1Shouling Ji, and Raheem Beyah
School of Electrical and Computer Engineering, Georgia Institute of
Technology
Zhipeng Cai
2
INTRODUCTION
The graph of relationships and interactions within a group of
individuals.
INFLUENCE
role as a medium for the spread of
INFLUENCE among its members
(facebook, twitter, myspace, …) 3
• the 3rd largest “Country” in the world
• More visitors than Google
• 2009, 2 billion tweets per quarter
• 2010, 4 billion tweets per quarter
•Action: Post tweets, Retweet
our really daily life and the virtual web space
5
social networks is a very important issue
and can benefit many real applications
– Advertising – Social recommendation – Expert finding
– Marketing
OUTLINE
Problem definition
Greedy Algorithm
Problem definition
Greedy Algorithm
Nodes start either active or inactive
An active node may trigger activation of neighboring nodes based on
a pre-defined threshold τ
Monotonicity assumption: active nodes never deactivate
9
OUTLINE
Problem definition
Greedy Algorithm
MODEL OF INFLUENCE
If u1 is active, then the active node set I = {u1}
P1(I) = 1
P2(I) = 0.5
P3(I) = 0.7
P4(I) = 0.6
12
If u1 and u4 are active, then the active node set I = {u1,
u4}
P1(I) = 1 – (1 – P11)(1 – P14) = 1
P2(I) = 1 – (1 – P21)(1 – P24) = 0.9
P3(I) = 1 – (1 – P31)(1 – P34) = 0.97
P4(I) = 1 – (1 – P41)(1 – P44) = 1
Pii = 1, if ui I
Pii = 0, otherwise
OUTLINE
Problem definition
Greedy Algorithm
Given
a threshold τ
by I could influence every node in the
network
Objective
OUTLINE
Problem definition
Greedy Algorithm
Greedy algorithm
Choose u to maximize f(I ∪ {u})
I = I ∪ {u}
Second round:
I = {u1}
I = {u2}
I = {u3}
I = {u4}
= 0.8
17
17
EXAMPLE
I = {u4 ,u2}
I = {u4 ,u3}
Use node ID to break the tie
I = {u4 ,u1}
f(I) = |V|τ = 4 * 0.8 = 3.2.
= 0.8
18
18
OUTLINE
Problem definition
Greedy Algorithm
OUTLINE
Problem definition
Greedy Algorithm
model G(n,p) = {G | G has n nodes, and an edge
between any pair of nodes is generated with
probability p}.
which is extracted from academic search system
Arnetminer [19].
of the key features of social networks more
generally.
554, 643distinct edges (coauthor relations)
23
OUTLINE
Problem definition
Greedy Algorithm
27
CONCLUSIONS
We introduce a new optimization problem, named the Minimum-sized
Influential Node Set (MINS) selection problem. We prove that it is
a NP-hard problem under the independent cascade model.
We define a polymatroid contribution function, which suggests us a
greedy approximation algorithm. Comprehensive theoretical analysis
about its performance ratio is given.
We conduct extensive experiments and simulations to validate our
proposed greedy algorithm both on real world coauthor data sets and
random graphs. 28
FUTURE WORK
Directed graph
Deal with negative influences
29
30