Abstract
The least cost influence maximization problem aims to determine minimum cost of partial (e.g., monetary) incentives initially given to the influential spreaders on a social network, so that these early adopters exert influence toward their neighbors and prompt influence propagation to reach a desired penetration rate by the end of cascading processes. We first conduct polyhedral analysis on a substructure that describes influence propagation assuming influence weights are unequal, linear and additively separable. Two classes of facet-defining inequalities based on a mixed 0–1 knapsack set contained in this substructure are proposed. We characterize another exponential class of valid and facet-defining inequalities utilizing the concept of minimum influencing subset. We show that these inequalities can be separated in polynomial time efficiently. Furthermore, a polynomial-time dynamic programming recursion is presented to solve this problem on a simple cycle graph. For arbitrary graphs, we propose a new exponential class of valid inequalities that dominates the cycle elimination constraints and an efficient separation algorithm for them. A compact convex hull description for a special case is presented. We illustrate the effectiveness of these inequalities via a delayed cut generation algorithm in the computational experiments.
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Data availability
The datasets analyzed during the current study are available from the corresponding author on reasonable request.
References
Ackerman E, Ben-Zwi O, Wolfovitz G (2010) Combinatorial model and bounds for target set selection. Theoret Comput Sci 411(44–46):4017–4022
Azaouzi M, Mnasri W, Romdhane LB (2021) New trends in influence maximization models. Comput Sci Rev 40:100393
Banerjee S, Jenamani M, Pratihar DK (2020) A survey on influence maximization in a social network. Knowl Inf Syst 62(9):3417–3455
Chen CL, Pasiliao EL, Boginski V (2020) A cutting plane method for least cost influence maximization. In: International Conference on Computational Data and Social Networks, pp. 499–511. Springer
Chen N (2009) On the approximability of influence in social networks. SIAM J Discret Math 23(3):1400–1415
Chen W, Lakshmanan LV, Castillo C (2013) Information and influence propagation in social networks. Synth Lect Data Manag 5(4):1–177
Dal Sasso V, De Giovanni L, Labbé M (2019) Strengthened formulations and valid inequalities for single delay management in public transportation. Transp Sci 53(5):1271–1286
Fischetti M, Kahr M, Leitner M, Monaci M, Ruthmair M (2018) Least cost influence propagation in (social) networks. Math Program 170(1):293–325
Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83(6):1420–1443
Grötschel M, Jünger M, Reinelt G (1985) On the acyclic subgraph polytope. Math Program 33(1):28–42
Günneç D, Raghavan S, Zhang R (2020) A branch-and-cut approach for the least cost influence problem on social networks. Networks 76(1):84–105
Günneç D, Raghavan S, Zhang R (2020) Least-cost influence maximization on social networks. INFORMS J Comput 32(2):289–302
Gursoy F, Günneç D (2018) Influence maximization in social networks under deterministic linear threshold model. Knowl-Based Syst 161:111–123
Hagberg AA, Schult DA, Swart PJ (2008) Exploring network structure, dynamics, and function using networkx. In: G. Varoquaux, T. Vaught, J. Millman (eds.) Proceedings of the 7th Python in Science Conference, pp. 11 – 15. Pasadena, CA USA
Keller B, Bayraksan G (2009) Scheduling jobs sharing multiple resources under uncertainty: a stochastic programming approach. IIE Trans 42(1):16–30
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, pp. 137–146
Kempe D, Kleinberg J, Tardos E (2015) Maximizing the spread of influence through a social network. Theory Comput 11(4):105–147
Li Y, Fan J, Wang Y, Tan KL (2018) Influence maximization on social graphs: a survey. IEEE Trans Knowl Data Eng 30(10):1852–1872
Loparic M, Marchand H, Wolsey LA (2003) Dynamic knapsack sets and capacitated lot-sizing. Math Program 95(1):53–69
Manzour H, Küçükyavuz S, Wu HH, Shojaie A (2021) Integer programming for learning directed acyclic graphs from continuous data. Informs J Optim 3(1):46–73
Marchand H, Wolsey LA (1999) The 0–1 knapsack problem with a single continuous variable. Math Program 85(1):15–33
Miller AJ, Nemhauser GL, Savelsbergh MW (2000) On the capacitated lot-sizing and continuous 0–1 knapsack polyhedra. Eur J Oper Res 125(2):298–315
Moazzez B, Soltani H (2018) Integer programming approach to static monopolies in graphs. J Comb Optim 35(4):1009–1041
Moazzez B, Soltani H (2021) Facets of the dynamic monopoly polytope: linear ordering formulation. Discret Optim 40:100641
Nannicini G, Sartor G, Traversi E, Wolfler Calvo R (2020) An exact algorithm for robust influence maximization. Math Program 183(1):419–453
Narisetty AK, Richard JPP, Nemhauser GL (2011) Lifted tableaux inequalities for 0–1 mixed-integer programs: a computational study. INFORMS J Comput 23(3):416–424
Peng S, Zhou Y, Cao L, Yu S, Niu J, Jia W (2018) Influence analysis in social networks: a survey. J Netw Comput Appl 106:17–32
Raghavan S, Zhang R (2021) Weighted target set selection on trees and cycles. Networks 77(4):587–609
Richard JP, de Farias Jr IR, Nemhauser GL (2003) Lifted inequalities for 0–1 mixed integer programming: basic theory and algorithms. Math Program 98(1):89–113
Richard JP, de Farias Jr IR, Nemhauser GL (2003) Lifted inequalities for 0–1 mixed integer programming: superlinear lifting. Math Program 98(1):115–143
Soltani H, Moazzez B (2019) A polyhedral study of dynamic monopolies. Ann Oper Res 279(1):71–87
Valente TW (1996) Social network thresholds in the diffusion of innovations. Social networks 18(1):69–89
Wu HH, Küçükyavuz S (2018) A two-stage stochastic programming approach for influence maximization in social networks. Comput Optim Appl 69(3):563–595
Acknowledgements
We are grateful to the two anonymous reviewers who provided constructive feedback that helped us improve the contents of this paper. We also thank Demetrios Papazaharias in the early discussion of the separation problem for the minimum influencing subset inequalities. This material is based upon work supported by the Air Force Research Laboratory (AFRL) Mathematical Modeling and Optimization Institute and AFRL award FA8651-16-2-0009. Preliminary results of this study were presented at the 9th International Conference on Computational Data and Social Networks (CSoNet 2020, December 11–13, 2020, Dallas, TX) and published in the respective conference proceedings volume (Chen et al. 2020).
Funding
This research was supported in part by AFRL award FA8651-16-2-0009.
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Chen, CL., Pasiliao, E.L. & Boginski, V. A polyhedral approach to least cost influence maximization in social networks. J Comb Optim 45, 44 (2023). https://doi.org/10.1007/s10878-022-00971-x
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DOI: https://doi.org/10.1007/s10878-022-00971-x