影響最大化(Influence maximization)是指透過一組種子節點來 進行訊息傳遞，最後達到整體訊息最大化。而現今在大型的社 群網路中，我們要求影響最大化演算法要同時滿足高精確度以 及高效率。傳統的貪婪演算法(greedy algorithm)具有高精確度， 但非常沒有效率。而其它啟發式(heuristic)的方法雖然高效率，但 卻不能保證精確度。本篇論文中，我們探討了貪婪演算法(greedy algorithm)的缺點，並分析其背後的原因。我們提出了固定子圖的 概念，並且結合子模性的性質，大大改善了效率。接著對演算法 做改良，實現超前部署，有機會能夠預先計算出下一回合該節點 的邊際影響(marginal influence)。最終我們的演算法達到了高準確 度高效率的結果。

Influence maximization is defined as using a seed set of nodes to spread information and finally achieve a maximized spread of influence. Nowadays, for large scale social networks, it is required that influence maximization algorithms should have both guaranteed accuracy and high efficiency. However, conventional greedy algorithms guarantee the accuracy but not the time efficiency. Though heuristic methods guarantee time efficiency, they still suffer from unstable accuracy. In this paper, We researched the shortcomings of the greedy algorithm and analyzed the reasons behind it. We proposed the concept of fixed subgraphs and using the property - submodularity. For the above concepts, we greatly improved efficiency. And then we made some improvements on the algorithm to achieve early deployment having the opportunity to precalculate the node’s marginal influence of the next round. Finally, our algorithm achieves high accuracy and efficiency.

中文摘要i
Abstract ii
Acknowledgements iii
List of Figures vi
List of Tables viii
1 Introduction 1
2 Related work 3
2.1 Independent Cascade Model . . . . . . . . . . . . . . . 3
2.2 Related research . . . . . . . . . . . . . . . . . . . 6
3 The dilemma of the greedy algorithm 9
3.1 Influence Maximization Problem . . . . . . . . . . . . . 9
3.2 Preserving Submodularity: the reason why the greedy algorithm so inefficient . . . . . . . . . . . . . . . . . . . 12
4 The Algorithm 14
4.1 Modified CELF . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Fixed subgraphs . . . . . . . . . . . . . . . . . . . . . 17
4.3 Our Algorithm . . . . . . . . . . . . . . . . . . . . . . 19
4.4 Analysis of our algorithm . . . . . . . . . . . . . . . . 27
4.4.1 Accuracy . . . . . . . . . . . . . . . . . . . . . 27
4.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . 32
5 Experiment 35
5.1 Experiment setup . . . . . . . . . . . . .. . . . . . . 35
5.2 Experiment results . . . . . . . . . . . . . . . . . .. 37
5.2.1 Influence spread comparison . . . . . . . . . . . 39
5.2.2 Computation time comparison . . . . . . . . . . 40
5.2.3 Memory consumption comparison . . . . . . . . 43
6 Conclusions 45
7 Appendix 46
Bibliography 49

[1] P. Domingos and M. Richardson, "Mining the network value of customers." In Proceedings of the 7th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2001.
[2] D. Kempe, J. M. Kleinberg, and É. Tardos, "Maximizing the spread of influence through a social network." In Proceedings of the 9th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2003.
[3] J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. VanBriesen, and N. Glance, “Cost-effective outbreak detection in networks.” 13th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, 2007
[4] C. Zhou, P. Zhang, W. Zang, and L. Guo, “On the upper bounds of spread for greedy algorithms in social network influence maximization.” IEEE Trans. Knowl. Data Eng., vol. 27, no. 10, Oct. 2015
[5] W. Chen, Y.Wang, and S. Yang, “Efficient influence maximization in social networks.” 15th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, 2009
[6] Y.Wang, G. Cong, G. Song, and K. Xie, “Community-based, greedy
algorithm for mining top-k influential nodes in mobile social networks.” 16th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, 2010
[7] S Kundu, SK Pal, "Deprecation based greedy strategy for target set selection in large scale social networks." Information Sciences Volume 316, 20 September 2015
[8] J Yuan, R Zhang, J Tang, R Hu, Z Wang, H Li, "Efficient and effective influence maximization in large-scale social networks via two frameworks." Physica A: Statistical Mechanics and its Applications Volume 526, 15 July 2019
[9] M Heidari, M Asadpour, H Faili, "SMG Fast scalable greedy algorithm for influence maximization in social networks." Physica A: Statistical Mechanics and its Applications Volume 420, 15 February 2015
[10] W. Chen, C.Wang, and Y.Wang, “Scalable influence maximization
for prevalent viral marketing in large-scale social networks.” 16th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, 2010
[11] M. Kimura, K. Saito, and R. Nakano, “Extracting influential nodes for information diffusion on a social network.” 22nd Nat. Conf. Artif. Intell. - Vol. 2, 2007
[12] K. Jung, W. Heo, and W. Chen, “IRIE: Scalable and robust influence maximization in social networks.” IEEE 12th Int. Conf. Data Mining, 2012
[13] WX Lu, C Zhou, J Wu, "Big social network influence maximization via recursively estimating influence spread." Knowledge-Based Systems Volume 113, 1 December 2016
[14] A Zareie, A Sheikhahmadi, K Khamforoosh, "Influence maximization in social networks based on TOPSIS." Expert Systems with Applications Volume 108, 15 October 2018
[15] F Lu, W Zhang, L Shao, X Jiang, P Xu, H Jin, "Scalable influence maximization under independent cascade model." Journal of Network and Computer Applications Volume 86, 15 May 2017
[16] Q Liqing, G Chunmei, Z Shuang, T Xiangbo, Zhang Mingjv,
"TSIM: A Two-Stage Selection Algorithm for Influence Maximization
in Social Networks." IEEE Access, 2020
[17] Z.-L. Luo, W.-D. Cai, Y.-J. Li, D. Peng, "A pagerank-based heuristic algorithm for influence maximization in the social network." LNEE, 2012
[18] G Tong, W Wu, S Tang, DZ Du, "Adaptive Influence Maximization
in Dynamic Social Networks." IEEE/ACM Transactions on Networking,
2017
[19] N Ohsaka, T Akiba, Y Yoshida, K Kawarabayashi, "Fast and Accurate Influence Maximization on Large Networks with Pruned Monte Carlo Simulations." AAAI Publications, Twenty-Eighth AAAI Conference on Artificial Intelligence, 2014
[20] E Cohen, D Delling, T Pajor, RFWerneck, "Sketch-based Influence Maximization and Computation: Scaling up with Guarantees." Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management, 2014
[21] S Cheng, H Shen, J Huang, W Chen, X Cheng, "IMRank Influence
Maximization via Finding Self-Consistent Ranking." Proceedings
of the 37th international ACM SIGIR conference on Research & development in information retrieval, 2014
[22] Q He, XWang, Z Lei,MHuang, Y Cai, L Ma, "TIFIM: A two-stage
iterative framework for influence maximization in social networks." Applied Mathematics and Computation , ELSEVIER, 2019
[23] Q Jiang, G Song, C Gao, Y Wang, W Si, K Xie, "Simulated Annealing Based Influence Maximization in Social Networks." Twenty- Fifth AAAI Conference on Artificial Intelligence, 2011
[24] C Tsai, Y Yang, M Chiang, "A Genetic NewGreedy Algorithm for Influence Maximization in Social Network." IEEE International
Conference on Systems, Man, and Cybernetics, 2015
[25] K Zhang, H Du, MW Feldman, "Maximizing influence in a social
network: Improved results using a genetic algorithm." Physica A:
Statistical Mechanics and its Applications, 2017
[26] S Peng, A Yang, L Cao, S Yu, D Xie, "Social influence modeling using information theory in mobile social networks." Information Sciences, 2017 - Elsevier
[27] S Cheng, H Shen, J Huang, G Zhang, XCheng, "StaticGreedy:
Solving the Scalability-Accuracy Dilemma in Influence Maximization." Proceedings of the 22nd ACM international conference on Information & Knowledge Management, 2014
[28] C. Borgs, M. Brautbar, J. Chayes, and B. Lucier, "Maximizing social influence in nearly optimal time." Proc. 25th Annu. ACM-SIAM Symp Discrete Algorithms, 2014
[29] Y. Tang, X. Xiao, and Y. Shi, "Influence maximization: Nearoptimal time complexity meets practical efficiency." Y. Tang, X. Xiao, and Y. Shi
[30] Y. Tang, Y. Shi, and X. Xiao, "Influence maximization in nearlinear time: A martingale approach." Proc. ACM SIGMOD Int. Conf. Manage. Data, 2015
[31] X. Wang, Y. Zhang, W. Zhang, X. Lin, and C. Chen "Bring order
into the samples: A novel scalable method for influence maximization." IEEE Trans. Knowl. Data Eng, 2017
[32] G Tong, W Wu, DZ Du, "Distributed Rumor Blocking With Multiple Positive Cascades." IEEE Transactions on Computational Social Systems, 2018
[33] M Li, F Liu, "Game Theory-Based Network Rumor Spreading
Model." International Conference on Network and Information Systems for Computers (ICNISC), 2016
[34] S Li, Y Zhu, D Li, D Kim, H Huang, "Rumor Restriction in Online Social Networks." IEEE 32nd International Performance Computing and Communications Conference (IPCCC), 2013
[35] C Budak, D Agrawal, A El Abbadi, "Limiting the Spread of Misinformation in Social Networks." Proceedings of the 20th international conference , WWW, 2011
[36] J Guo, P Zhang, C Zhou, Y Cao, L Guo, "Personalized Influence
Maximization on Social Networks." Proceedings of the 22nd ACM
international conference on Information & Knowledge Management
[37] Y Li, D Zhang, "Realtime Targeted Influence Maximization for Online Advertisements." Proceedings of the VLDB Endowment, 2015
[38] T Zhou, J Cao, B Liu, S Xu, Z Zhu, J Luo, "Location-Based Influence Maximization in Social Networks." Proceedings of the 24th ACM International on Conference on Information and Knowledge
Management
[39] G Li, S Chen, J Feng, K Tan, W Li, "Efficient location-aware influence maximization." Proceedings of the 2014 ACM SIGMOD International Conference, 2014
[40] CELF graph for influence maximization problem,
"https://www.cnblogs.com/aaronhoo/p/6548760.html"
[41] Network Repository Datasets [Online], Available:
"http://networkrepository.com/index.php"
[42] SNAP Datasets: Stanford Large Network Dataset Collection. [Online]. Available: http://snap.stanford.edu/data
[43] A Arora, S Galhotra, S Ranu, "Debunking the Myths of Influence Maximization: An In-Depth Benchmarking Study." SIGMOD Proceedings of the 2017 ACM International Conference, 2017
[44] Y Li, J Fan, Y Wang, K Tan, "Influence maximization on social
graphs: A survey." IEEE Transactions on Knowledge and Data Engineering, 2018