IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 3, MARCH 2017 2789
Cost-Efficient Strategies for Restraining Rumor
Spreading in Mobile Social Networks
Zaobo He, Student Member, IEEE, Zhipeng Cai, Senior Member, IEEE, Jiguo Yu, Xiaoming Wang,
Yunchuan Sun, Senior Member, IEEE, and Yingshu Li, Senior Member, IEEE
Abstract—With the popularity of mobile devices, mobile social
networks (MSNs) have become an important platform for infor-
mation dissemination. However, the spread of rumors in MSNs
present a massive social threat. Currently, there are two kinds of
methods to address this: blocking rumors at influential users and
spreading truth to clarify rumors. However, most existing works
either overlook the cost of various methods or only consider dif-
ferent methods individually. This paper proposes a heterogeneous-
network-based epidemic model that incorporates the two kinds
of methods to describe rumor spreading in MSNs. Moreover, two
cost-efficient strategies are designed to restrain rumors. The first
strategy is the real-time optimization strategy that minimizes the
rumor-restraining cost by optimally combining various rumor-
restraining methods such that a rumor can be extinct within an
expected time period. The second strategy is the pulse spread-
ing truth and continuous blocking rumor strategy that restrains
rumor spreading through spreading truth periodically. The two
strategies can restrain rumors in a continuous or periodical man-
ner and guarantee cost efficiency. The experiments toward the
Digg2009 data set demonstrate the effectiveness of the proposed
model and the efficiency of the two strategies.
Index Terms—Blocking rumors, maximum immunization
period, Pontryagin’s maximum principle, pulse immunization,
spreading truth.
I. INTRODUCTION
W
ITH the advance of mobile communication technology,
mobile social networks (MSNs) are providing diverse
services through interconnecting mobile devices and social net-
works. Unfortunately, MSNs also pave the way for the spread
of rumors, unverified claims, and other k inds of disinformation.
It has been shown that rumors spread much faster in MSNs
than in other networks and cause more severe consequences [1].
Manuscript receive d January 2, 2016; revised April 25, 2016; accepted
June 4, 2016. Date of publication June 28, 2016; date of current version
March 10, 2017. This work was supported in part by the National Science Foun-
dation (NSF) under Grant CNS-1252292; by the NSF of China under Grant
61373083, Grant 61370084, Grant 61502116, Grant 61371185, and Grant
61373027; by the NSF of Shandong Province under Grant ZR2012FM023; and
by the China Postdoctoral Science Foundation under Grant 2015M571231. The
re view of this paper was coordinated by Prof. J. Sun. (Corresponding author:
Xioming Wang .)
Z. He, Z. Cai, and Y. Li are with the Department of Computer Science,
Georgia State University, Atlanta, GA 30302 USA (e-mail: zhe4@student.gsu.
edu; zcai@gsu.edu; yili@gsu.edu).
J. Yu is with the School of Information Science and Engineering, Qufu
Normal University, Rizhao 276826, China (e-mail: jiguoyu@sina.com).
X. Wang is with the School of Computer Science, Shaanxi Normal Univer-
sity, Xi’an 710119, China (e-mail: wangxm@snnu.edu.cn).
Y. Sun is with the Business School, Beijing Normal University, Beijing
100875, China (e-mail: yunch@bnu.edu.cn).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2016.2585591
For example, on April 23, 2013, the rumor “Two bombs had
exploded at the White House and Barack Obama is injured”
spread on Twitter and caused the United States stock market to
crash in a few minutes [2].
Currently, there are two kinds of methods for restraining
rumor spreading in MSNs: blocking rumors at in fluential users
[3]–[6] and spreading truth to clarify rumors [7], [8]. Unfor-
tunately, the costs to carry out these two methods are usually
overlooked [5], [9]. The first kind of method may violate human
rights, and persuading someone to abandon her current opinion
is tedious work. Hence, the first kind of methods generally
needs various resources such as incentives, supported docu-
ments, and so forth. Similarly, spreading truth needs cooper-
ation with social media and requires several network resources
such as channels. For simplicity, we denote blocking rumors at
influential users and spreading truth to clarify rumors as immu-
nization and cure in the rest of this paper without confusion,
respectively. Moreover, immunization and cure are individually
considered in most existing works [3]–[6]. Hence, prior works
overestimate the efficiency o f the designed countermeasures
and are costly. In this paper, we present two strategies to
restrain rumor spreading, both of which consider immunization
and cure with limited costs. We first propose a real-time opti-
mization (RTO) strategy that minimizes the rumor-restraining
cost by optimally combining im munization and cure so that a
rumor can be extinct within an expected time period. With the
optimization objective, RTO provides the optimized rates for
immunization and cure in a real-time manner. Clearly, RTO re-
quires immunization and cure to be continuously conducted in a
period. That is, at any time t, t ∈ [0,t
f
] where t
f
is an expected
time period, both immunization and cure should be carried
out with certain rates. Clearly, RTO needs to occupy rumor-
restraining resources continuously since it continuously spreads
truth to immunize susceptible users (i.e., immunization). How-
ever, it is challenging, sometimes impossible, to continuously
consume the limited resources in a period amon g multiparties.
Therefore, this challenge motivates us to propose the pulse
spreading truth and continuous blocking rumor (PSCB) strategy
that carries out immunization in a periodical manner. Therefore,
we propose the PSCB strategy that restrains rumor spreading by
spreading truth periodically. PSCB intends to find a maximum
period so that the cost of spreading truth can be reduced. We de-
note such a period as the maximum immunization period.RTO
is applicable when rumor-restraining resources are enough and
rumor s are intended to be restrained within a certain time pe-
riod. Comparatively, PSCB is applicable when resources are not
enough and when there is no specific time limitation to restrain
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