An Efficient Randomized Algorithm for Rumor
Blocking in Online Social Networks
Guangmo (Amo) Tong
∗
, Weili Wu
†∗¶
, Ling Guo
‡
, Deying Li
‡
, Cong Liu
∗
, Bin Liu
§
and Ding-Zhu Du
∗
∗
Dept. of Computer Science, University of Texas at Dallas, USA
†
Taiyuan University of Technology, China
‡
Renmin University, China
§
Ocean University of China, China
¶
Corresponding author
{guangmo.tong, cxl131130, weiliwu, cxl137330, dzdu}@utdallas.edu
{guoling, deyingli}@ruc.edu.cn, binliu@ouc.edu.cn
Abstract—Social networks allow rapid spread of ideas and
innovations while the negative information can also propagate
widely. When the cascades with different opinions reaching the
same user, the cascade arriving first is the most likely to be taken
by the user. Therefore, once misinformation or rumor is detected,
a natural containment method is to introduce a positive cascade
competing against the rumor. Given a budget k, the rumor
blocking problem asks for k seed users to trigger the spread of the
positive cascade such that the number of the users who are not
influenced by rumor can be maximized. The prior works have
shown that the rumor blocking problem can be approximated
within a factor of (1 − 1/e − δ) by a classic greedy algorithm
combined with Monte Carlo simulation with the running time
of O(
k
3
mn ln n
δ
2
), where n and m are the number of users and
edges, respectively. Unfortunately, the Monte-Carlo-simulation-
based methods are extremely time consuming and the existing
algorithms either trade performance guarantees for practical
efficiency or vice versa. In this paper, we present a randomized
algorithm which runs in O(
km ln n
δ
2
) expected time and provides
a (1 − 1/e − δ)-approximation with a high probability. The
experimentally results on both the real-world and synthetic
social networks have shown that the proposed randomized rumor
blocking algorithm is much more efficient than the state-of-the-
art method and it is able to find the seed nodes which are effective
in limiting the spread of rumor.
I. INTRODUCTION
The tremendous advance of the Internet of things (loT)
is making the online social networks be the most common
platform for communication. There have been totally 44.5
million users on Twitter and 1.4 million monthly active
users on Facebook. Admittedly the online social networks are
greatly beneficial, they also lead the widespread of negative
information. Such negative influence, namely misinformation
and rumor, has been a cause of concern as it renders the
network unreliable and may cause further panic in population.
For example, the misinformation of swine flu in Twitter threw
the people in Texas and Kansas into panic in 2009 [1], and
the endless report of Ebola in 2014 has caused unnecessary
worldwide terror. Therefore, effective strategies for rumor
containment are crucial for social networks and it has been
a hot topic in the last decades.
In a social network, information and innovations diffuse
from user to user via influence cascades where each cascade
starts to spread with a set of seed users. When two cascades
holding opposing views reach a certain user, the user is likely
to trust the cascade arriving first. For the example of swine
flu, if the international institutions like WHO would have
posts clarification for swine flu, the users who have read such
posts will not be influenced by the misinformation. Therefore,
the most common method for rumor blocking is to generate
a corresponding positive cascade that competes against the
rumor. Due to the expense of deploying seed nodes, there is
a budget k for the positive cascade, and naturally one should
select the k positive seed nodes such that the number of rumor-
activated users is minimized, which is referred as the least cost
rumor blocking problem.
The recent study of influence diffusion process in social
networks can be tracked back to D. Kempe [2] where the
well-known influence maximization problem is formulated. In
that seminal work, two fundamental probabilistic operational
models, independent cascade (IC) model and linear threshold
(LT) model are developed. Based on such models, many
influence related problems are then proposed and studied.
The problem of rumor blocking is also considered in such
models or in their variants. Most existing approaches utilize
the submodularity of the objective function. That is, the
number of non-rumor-activated users is a monotone increasing
submodular function and therefore the classic hill-climbing al-
gorithm provides a (1 − 1/e)-approximation [3]. For example,
X. He et al. [4] formulate the influence blocking maximization
problem and show a (1−1/e)-approximation algorithm for the
competitive linear threshold model, Budak et al. [5] propose
several competitive models and show a greedy algorithm with
the same approximation ratio under the campaign-oblivious
independent cascade model, and, Fan et al. [6] provide a
(1 − 1/e)-approximation algorithm for the rumor blocking
problem under the opportunistic one-active-one model.
Assuming that the objective function can be efficiently
1
calculated for any input, the greedy algorithm is simple and
effective for most of the submodular maximization problems.
Unfortunately, for the influence related optimization problems,
1
Usually this is referred to the polynomial-time computability.
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