Elsevier

Computer Communications

Volume 182, 15 January 2022, Pages 41-51
Computer Communications

Fast controlling of rumors with limited cost in social networks

https://doi.org/10.1016/j.comcom.2021.10.041Get rights and content

Abstract

Innumerable rumors spread quickly through social networks and how to fast control the spread of rumors is crucial. An efficient way is to take different measures for users with different influence extent by rumors, but the costs of these measures vary. In this paper, we try to minimize the spread (termination) time of rumors considering the controlling cost. To solve this problem, we creatively design five different measures to control rumors. First, we propose a contact coefficient to quantify the influence weight for each user. Second, we classify the users to different groups based on their influence weights so that the rumors can be controlled by the measures accordingly. Thus, the controlling of rumors can be formulated into an optimization problem, in which decision variables based on contact coefficients are used to classify users. Then an approximation algorithm named WB-GA is designed to classify different users, ensuring that rumors can be controlled as fast as possible within given costs. The experimental results on real online networks show that our algorithm is highly efficient and effective.

Introduction

With the growing popularity of online social networks, information can spread faster and more widely than ever before. Meanwhile, the establishment of such an environment facilitates the spreading of rumors. Rumors are often defined as unverified statements [1], [2] that might be eventually found as true or false. For example, a disaster swept the whole world and there came a lot of rumors, which can spread much faster than the disaster itself, causing more damage. It is conceivable that there will be huge economic losses and even society instability if not stopping the spreading of rumors in time. Therefore, fast controlling of rumors is urgent and necessary in social networks.

In literature, the commonly used methods to control the rumors can be divided into three categories: (1) Removing associations between users to block rumors [3], [4], [5]; (2) Blocking influential users [6], [7], [8]; (3) Spreading truth to clarify rumors [9], [10], [11]. In addition, B. Wang et al. [12] in a recent work introduce experiences into rumor controlling, and G. Tong et al. [13] propose a fast randomized approximation to control rumors. However, all of these studies just take one measure in rumor controlling.

In reality, the extent that users are influenced by rumors can be quite different, and the best way to control the rumors is to take different measures for the users. For example, for those users who are influenced by rumors or even want to continue to spread rumors, we should stop this process by deleting their accounts. For those users who have a high probability of being influenced by rumors, we should spread truth to them or block them from accessing information. For those users who have a low probability of being influenced by rumors, we just need to tag and track them. In view of this, we propose to classify the users into different groups with different controlling measures. To be practical, we rank users from lowest to highest probability of being influenced by rumors and we consider classifying users into 5 groups (H1, H2, H3, H4, H5) with measures of taking no action, tagging the user, blocking access to information, spreading the truth, deleting the user’s account, respectively. Note that, the cost of these measures are different. We aim to use different control measures with limited cost to control rumors as fast as possible. In order to quantify the influence weight for each user, we use a contact coefficient to classify the users.

In this paper, we study the problem of fast controlling of rumors (called FCR problem) in a social network with limited cost by using different controlling measures. Note that, the spread time of rumors is defined as the time when all rumors terminate in the spreading process. Given the total cost, our goal is to minimize the spread time of rumors under the constraint of cost. The decision variables are the classifying boundaries of each group based on the contact coefficient. The classifying boundary for each group refers to the maximum and minimum contact coefficients of users in each group.

The main contributions of this paper are presented as follows:

We creatively propose to classify users to different groups with five measures for rumor controlling, which is of great significance in practice. The five different measures are taking no action, tagging the user, blocking access to information, spreading the truth and deleting the user’s account.

We propose a Multi-Probability Independent Cascade (MPIC) model to describe the process of spreading rumors. We also propose a well-designed contact coefficient and model the controlling of rumors into an optimization problem.

We design a Withdraw Bedeckung-Greedy Algorithm named as WB-GA to solve this problem. After a series of theoretical analysis, we prove that the data-parameter-based approximation ratio of the WB-GA is more than log(1p(u,v)+α3)(1p(u,v)+α2), where p(u,v) is the influence probability for each edge without taking any measure, α2 is the blocking influence rate of H2 and α3 is the blocking influence rate of H3.

Numerical experiments are conducted to evaluate the performance of our algorithm. Under the datasets of real online networks including Lastfm-social and Deezer-social, the performances of WB-GA are superior to that of the comparison methods.

The rest of this paper is organized as follows. Section 2 reviews related work. In Section 3, we formulate the controlling of rumors into an optimization problem. Section 4 give the details of our algorithm WB-GA. In Section 5, we conduct theoretical analysis of the problem and the algorithm. In Section 6, we make evaluations through extensive experiments. Finally, we conclude the whole paper in Section 7.

Section snippets

Related work

So far, there have been much work on rumor detection [14], [15], [16], [17]. S. Kwon et al. [18] and J. Ma et al. [19] propose handcrafted-features based algorithms to detect rumors. F. Yu et al. [20] and J. Ma et al. [21] propose deep-learning based methods using Gated Recurrent Unit (GRU) and Convolutional Neural Network (CNN).

There are also a lot of scholars [22], [23], [24] studying the controlling of rumors. H. Jing et al. [25] and X. Liu et al. [26] try to identify a set of target nodes

Problem model

In this section, we first introduce the preliminaries of this paper, and then give the problem model in detail. The notations and definitions to be used are listed in Table 1.

Proposed method

In this section, we design a Withdraw Bedeckung-Greedy Algorithm (WB-GA) for finding the shortest τ in social networks. In proposed WB-GA algorithm, let hi(i=1,2,,) denote the number of nodes with the same contact coefficient, as shown in Algorithm 1.

In Algorithm 1, we find the θ1,θ2,θ3 based on contact coefficient. We rank nodes with the same contact coefficient in descending order and put the True nodes into H5. Case 1, we randomly select different θ1,θ2,θ3 to satisfy serveral conditions.

Theoretical analysis

In this section, we conduct theoretical analysis on the properties of FCR problem and algorithm WB-GA.

Theorem 1

Let ft be the expected number of True nodes when the spread is over at time t, then calculating the ft is #P-hard.

Proof

As shown in [36] that st connectedness problem is #P-complete. Based on [37], this problem is equivalent to calculating the probability of connecting two nodes when each edge in G is connected with a probability of 1/2.

Then we reduce this problem to calculating ft as follows. Let ft

Datasets and parameters

We select two real social networks from SNAP1 and use them to evaluate the effectiveness of our algorithm.

(1) Lastfm-social: It is an online social network of LastFM users, which is collected from the public API in March 2020. Nodes are LastFM users from Asian countries and edges are relationships between them. Its density is 0.001.

(2) Deezer-social: It is an online social network of Deezer users, which is collected from the public API in March 2020. Nodes are Deezer

Conclusions

In this paper, we study the problem of fast controlling of rumors (FCR) problem in social networks. First, we propose five measures for different users to control rumors, including taking no action, tagging the user, blocking access to information, spreading the truth and deleting the user’s account. Taking five measures to control rumors is more realistic and effective than taking only one. Second, based on the IC model, we propose a MPIC model to describe the process of spreading rumors. This

CRediT authorship contribution statement

Xiaopeng Yao: Investigation, Conceptualization, Methodology, Design algorithm, Prove theories, Writing draft. Yue Gu: Generate some figures, Design algorithm and programming, Put forward some corollaries. Chonglin Gu: Algorithm improvement, Optimization of time complexity and algorithm, Revise the paper. Hejiao Huang: Put forward ideas, Discuss and optimize algorithm and method, Revise the paper.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is financially supported by Shenzhen Science and Technology Program under Grant No. JCYJ20210324132406016 and National Natural Science Foundation of China under Grant No. 61732022, China Postdoctoral Science Foundation under Grant No. 2020T130633, Guangdong Basic and Applied Basic Research Foundation, China under Grant No. 2019A1515110214 and Initial Scientific Research Fund of HITSZ, China with Grant No. BB45001011.

References (40)

  • H. Habiba, Y. Yu, T.Y. Berger-Wolf, J. Saia, Finding spread blockers in dynamic networks, in: Proc. SNAKDD (2010) pp....
  • S. Wang, X. Zhao, Y. Chen, Z. Li, J. Xia, Negative influence minimizing by blocking nodes in social networks, in: Proc....
  • TanZ. et al.

    Aim: Activation increment minimization strategy for preventing bad information diffusion in OSNs

    Future Gener. Comput. Syst.

    (2018)
  • WangB. et al.

    DRIMUX: DYnamic rumor influence minimization with user experience in social networks

    IEEE Trans. Knowl. Data Eng.

    (2017)
  • TongG. et al.

    An efficient randomized algorithm for rumor blocking in online social networks

    IEEE Trans. Netw. Sci. Eng.

    (2020)
  • Y. Liu, X. Chen, Y. Rao, H. Xie, Q. Li, J. Zhang and, et al. Supervised group embedding for rumor detection in social...
  • T. Takahashi, N. Igata, Rumor detection on Twitter, in: Proc. 6th Int. Conf. Soft Comput. Intell. Syst and 13th Int....
  • Z. Wang, W. Dong, W. Zhang, C.W. Tan, Rumor source detection with multiple observations: Fundamental limits and...
  • V. Qazvinian, E. Rosengren, D.R. Radev, Q. Mei, Rumor has it: Identifying misinformation in microblogs, in: Proc. Conf....
  • S. Kwon, M. Cha, K. Jung, W. Chen, Y. Wang, Prominent features of rumor propagation in online social media, in: Proc....
  • Cited by (8)

    • Influence blocking maximization on networks: Models, methods and applications

      2022, Physics Reports
      Citation Excerpt :

      Therefore, rumor propagation is mainly based on the classical epidemic model or its improved versions [10,11,50,54,162,163]. Rumor suppression algorithms mainly include the methods of blocking rumor nodes [14,58,61,63,64,69,72,73], blocking rumor links [8,23,24,75–77,80,83,160,164] and suppressing rumor through positive influence [5,6,38,87,165–169]. He et al. [168] proposed a real-time optimization strategy that enables to suppress the spread of rumors at a minimum cost within the expected time period.

    • Research on homogeneous information propagation in social network

      2023, International Journal of Modern Physics C
    View all citing articles on Scopus
    View full text