Skip to main content
SpringerLink
Log in

A numerical evaluation of the accuracy of influence maximization algorithms

  • Original Article
  • Published:
Social Network Analysis and Mining Aims and scope Submit manuscript

Abstract

We develop an algorithm to compute exact solutions to the influence maximization problem using concepts from reverse influence sampling (RIS). We implement the algorithm using GPU resources to evaluate the empirical accuracy of theoretically guaranteed greedy and RIS approximate solutions. We find that the approximations yield solutions that are remarkably close to optimal—usually achieving greater than 99% of the optimal influence spread. This accuracy is consistent across a wide range of network structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. “Exact” solutions in this article will technically be \((1-\epsilon )\) approximations, which is consistent with the use of that term in much of the literature (Li et al. 2017, 2019).

  2. We assume \(p_e=p\), \(\forall e\) throughout.

  3. This is Lemma 1 in, for example, Huang et al. (2017).

  4. The value of \(\theta \) determines both the runtime of the algorithm and \(\epsilon \). However, the relationship between \(\theta \) and \(\epsilon \) is a function of the optimal solution, as shown in Theorem 1. The literature has focused on determining increasingly tighter values of \(\theta \) to reduce the runtime through various techniques like limiting the total number of edges examined during the generation process to a pre-defined threshold (Borgs et al. 2014), using Chernoff bounds (Tang et al. 2014) and adopting martingale methods (Tang et al. 2015), among others (Nguyen et al. 2016; Huang et al. 2017). We focus on the two computational steps common to all RIS methods and set \(\theta =100{,}000\). Because this affects both the approximate and exact solutions equally, the proportional difference between the solutions is approximately independent of \(\theta \) so long as it ensures \(\epsilon<< e\), which it trivially does.

  5. Examples of various versions of this lemma in the literature are Lemma 3 in Tang et al. (2014), Lemma 3 in Tang et al. (2015), and Lemma 5 in Nguyen et al. (2016).

  6. The \(\beta =1\) version is not identical to the Erdős–Rényi model because it enforces each node to have at least K/2 connections, whereas there is no restriction on edges for a given node in Erdős–Rényi.

  7. The Python code to generate all results is available at https://github.com/hautahi/IM-Evaluation.

References

  • Akbarpour M, Malladi S, Saberi A (2018) Diffusion, seeding, and the value of network information. In: Proceedings of the 2018 ACM conference on economics and computation. ACM, pp 641–641

  • Albert R, Jeong H, Barabási A-L (2000) Error and attack tolerance of complex networks. Nature 406(6794):378

    Article  Google Scholar 

  • Bader DA, Madduri K (2008) Snap, small-world network analysis and partitioning: an open-source parallel graph framework for the exploration of large-scale networks. In: 2008 IEEE international symposium on parallel and distributed processing. IEEE, pp 1–12

  • Barabási A-L, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509–512

    Article  MathSciNet  Google Scholar 

  • Barnat J, Bauch P, Brim L, Ceska M (2011) Computing strongly connected components in parallel on cuda. IEEE Int Parallel Distrib Process Sympos 2011:544–555

    Google Scholar 

  • Basaras P, Katsaros D (2019) Identifying influential spreaders in complex networks with probabilistic links. In: Social networks and surveillance for society. Springer, Cham, pp 57–84

    Chapter  Google Scholar 

  • Bollobás B, Riordan O (2004) Robustness and vulnerability of scale-free random graphs. Internet Math 1(1):1–35

    Article  MathSciNet  Google Scholar 

  • Borgs C, Brautbar M, Chayes J, Lucier B (2014) Maximizing social influence in nearly optimal time. In: Proceedings of the twenty-fifth annual ACM-SIAM symposium on discrete algorithms. SIAM, pp 946–957

  • Chen W, Wang Y, Yang S (2009) Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 199–208

  • Chen W, Wang C, Wang Y (2010) Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 1029–1038

  • Chen D-B, Xiao R, Zeng A (2014) Predicting the evolution of spreading on complex networks. Sci Rep 4:6108

    Article  Google Scholar 

  • Cohen R, Erez K, Ben-Avraham D, Havlin S (2000) Resilience of the internet to random breakdowns. Phys Rev Lett 85(21):4626

    Article  Google Scholar 

  • Domingos P, Richardson M (2001) Mining the network value of customers. In: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 57–66

  • Domingos P, Richardson M (2002) Mining knowledge-sharing sites for viral marketing. In: Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 61–70

  • Emami N, Mozafari N, Hamzeh A (2018) Continuous state online influence maximization in social network. Soc Netw Anal Min 8(1):32

    Article  Google Scholar 

  • Erdős P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5(1):17–60

    MathSciNet  MATH  Google Scholar 

  • Galhotra S, Arora A, Roy S (2016) Holistic influence maximization: combining scalability and efficiency with opinion-aware models. In: Proceedings of the 2016 international conference on management of data. ACM, pp 743–758

  • Goyal A, Lu W, Lakshmanan LV (2011) Celf++: optimizing the greedy algorithm for influence maximization in social networks. In: Proceedings of the 20th international conference companion on world wide web. ACM, pp 47–48

  • Harish P, Narayanan P (2007) Accelerating large graph algorithms on the GPU using CUDA. In: International conference on high-performance computing. Springer, pp 197–208

  • He X, Kempe D (2016) Robust influence maximization. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp 885–894

  • Huang K, Wang S, Bevilacqua G, Xiao X, Lakshmanan L (2017) Revisiting the stop-and-stare algorithms for influence maximization. Proc VLDB Endow 10:913–924

    Article  Google Scholar 

  • Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence through a social network. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 137–146

  • Kim J, Kim SK, Yu H (2013) Scalable and parallelizable processing of influence maximization for large-scale social networks? In: IEEE 29th international conference on data engineering (ICDE). IEEE, pp 266–277

  • LaSalle D, Karypis G (2013) Multi-threaded graph partitioning. In: IEEE 27th international symposium on parallel and distributed processing. IEEE, pp 225–236

  • Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, Glance N (2007) Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 420–429

  • Li X, Smith JD, Dinh TN, Thai MT (2017) Why approximate when you can get the exact? Optimal targeted viral marketing at scale. In: IEEE INFOCOM 2017-IEEE conference on computer communications. IEEE, pp 1–9

  • Li X, Smith JD, Dinh TN, Thai MT (2019) Tiptop:(almost) exact solutions for influence maximization in billion-scale networks. IEEE/ACM Trans Netw 27(2):649–661

    Article  Google Scholar 

  • Liu X, Li M, Li S, Peng S, Liao X, Lu X (2013) Imgpu: GPU-accelerated influence maximization in large-scale social networks. IEEE Trans Parallel Distrib Syst 25(1):136–145

    Google Scholar 

  • Marro J, Dickman R (2005) Nonequilibrium phase transitions in lattice models. Cambridge University Press, Aléa-Saclay

    MATH  Google Scholar 

  • Molloy M, Reed B (1995) A critical point for random graphs with a given degree sequence. Random Struct Algorithms 6(2–3):161–180

    Article  MathSciNet  Google Scholar 

  • Moore C, Newman ME (2000) Epidemics and percolation in small-world networks. Phys Rev E 61(5):5678

    Article  Google Scholar 

  • More J, Lingam C (2019) A gradient-based methodology for optimizing time for influence diffusion in social networks. Soc Netw Anal Min 9(1):5

    Article  Google Scholar 

  • Morone F, Makse HA (2015) Influence maximization in complex networks through optimal percolation. Nature 524(7563):65

    Article  Google Scholar 

  • Newman ME (2001) Clustering and preferential attachment in growing networks. Phys Rev E 64(2):025102

    Article  Google Scholar 

  • Nguyen HT, Thai MT, Dinh TN (2016) Stop-and-stare: optimal sampling algorithms for viral marketing in billion-scale networks. In: Proceedings of the 2016 international conference on management of data. ACM, pp 695–710

  • Pastor-Satorras R, Vespignani A (2001) Epidemic dynamics and endemic states in complex networks. Phys Rev E 63(6):066117

    Article  Google Scholar 

  • Piraveenan M, Harré M, Kasthurirathna D (2016) Optimising influence in social networks using bounded rationality models. Soc Netw Anal Min 6:54

    Article  Google Scholar 

  • Srivastava A, Chelmis C, Prasanna V (2015) The unified model of social influence and its application in influence maximization. Soc Netw Anal Min 5:66

    Article  Google Scholar 

  • Tang Y, Xiao X, Shi Y (2014) Influence maximization: near-optimal time complexity meets practical efficiency. In: Proceedings of the 2014 ACM SIGMOD international conference on management of data. ACM, pp 75–86

  • Tang Y, Shi Y, Xiao X (2015) Influence maximization in near-linear time: a martingale approach. In: Proceedings of the 2015 ACM SIGMOD international conference on management of data. ACM, pp 1539–1554

  • Tang J, Tang X, Yuan J (2018) An efficient and effective hop-based approach for influence maximization in social networks. Soc Netw Anal Min 8:10

    Article  Google Scholar 

  • Tsugawa S, Ohsaki H (2018) Robustness of influence maximization against non-adversarial perturbations. In: IEEE/ACM international conference on advances in social networks analysis and mining. Springer, Cham, pp 193–210

  • Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facebook Inc, New York, NY, USA

    Hautahi Kingi

  2. Sam Houston State University, Huntsville, TX, USA

    Li-An Daniel Wang

  3. Elder Research, Inc, Raleigh, NC, USA

    Tom Shafer

  4. IMPAQ International, Washington DC, USA

    Minh Huynh

  5. IMPAQ International, Boston, MA, USA

    Mike Trinh

  6. Northeastern University, Boston, MA, USA

    George Rochester

  7. U.S. Food and Drug Administration, Silverspring, MD, USA

    Antonio Paredes

  8. IMPAQ International, Columbia, MD, USA

    Aaron Heuser

Authors
  1. Hautahi Kingi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li-An Daniel Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tom Shafer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minh Huynh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mike Trinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Aaron Heuser
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. George Rochester
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Antonio Paredes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hautahi Kingi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kingi, H., Wang, LA.D., Shafer, T. et al. A numerical evaluation of the accuracy of influence maximization algorithms. Soc. Netw. Anal. Min. 10, 70 (2020). https://doi.org/10.1007/s13278-020-00680-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13278-020-00680-5

Keywords

Search

Navigation