Abstract
In this paper, we show several results about the strict submodularity of the influence spread in a social network with general threshold model if at each node, the threshold function is strictly increasing and strictly submodular.
Similar content being viewed by others
References
Gu S, Shi G, Wu W, Lu C (2020) A fast double greedy algorithm for non-monotone DR-submodular function maximization. Discrete Math Alg Appl 12(1):2050007:1–2050007:11
Iyer R, Bilmes J (2012) Algorithms for approximate minimization of the difference between submodular functions. In: Proceedings of UAI
Kempe D, Kleinberg JM, Tardos E (2003) Maximizing the spread of influence through a social network. In: KDD, pp 137–146
Lei L, Ni Qiufen L, Changhong HC, Weili W (2019) Monotone submodular maximization over the bounded integer lattice with cardinality constraints. Discrete Math Alg Appl 11(6):1950075:1–1950075:14
Li X, Du HG, Pardalos PM (2020) A variation of DS decomposition in set function optimization. J Combin Optim 40(1):36–44
Li X, Du HG (2020) A short proof for stronger version of DS decomposition in set function optimization. J Combin Optim. https://doi.org/10.1007/s10878-020-00639-4
Mossel E, Roch S (2007) On the submodularity of influence in social networks. In: STOC’2007, pp 128–134.c
Narasimhan M, Bilmes J (2005) A submodular-supermodular procedure with applications to discriminative structure learning. In: Proceedings of UAI
Nemhauser GL, Wolsey LA, Fisher ML (1978) An analysis of approximations for maximizing submodular set functions—I. Math Program 14(1):265–294
Weili W, Hongwei D, Wang H, Lidong W, Duan Z, Tian C (2018) On general threshold and general cascade models of social influence. J Combin Optim 35(1):209–215
Weili W, Zhang Z, Ding-Zu D (2019) Set function optimization. J Oper Res Soc China 7(2):183–193
Acknowledgements
This work is supported in part by National Natural Science Foundation of China (No. 61772154) and the Shenzhen Basic Research Program (Project No. JCYJ2019080614 3011274).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ni, Q., Du, H. On strict submodularity of social influence. J Comb Optim 41, 348–356 (2021). https://doi.org/10.1007/s10878-020-00683-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-020-00683-0