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Think Globally, Act Locally: On the Optimal Seeding for Nonsubmodular Influence Maximization

Authors Grant Schoenebeck , Biaoshuai Tao , Fang-Yi Yu

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Author Details

Grant Schoenebeck
  • University of Michigan, Ann Arbor, USA
Biaoshuai Tao
  • University of Michigan, Ann Arbor, USA
Fang-Yi Yu
  • University of Michigan, Ann Arbor, USA

Funding

  • Schoenebeck, Grant: National Science Foundation AitF #1535912 and CAREER #1452915
  • Tao, Biaoshuai: National Science Foundation CAREER #1452915
  • Yu, Fang-Yi: National Science Foundation AitF #1535912

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Grant Schoenebeck, Biaoshuai Tao, and Fang-Yi Yu. Think Globally, Act Locally: On the Optimal Seeding for Nonsubmodular Influence Maximization. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.39

Abstract

We study the r-complex contagion influence maximization problem. In the influence maximization problem, one chooses a fixed number of initial seeds in a social network to maximize the spread of their influence. In the r-complex contagion model, each uninfected vertex in the network becomes infected if it has at least r infected neighbors. In this paper, we focus on a random graph model named the stochastic hierarchical blockmodel, which is a special case of the well-studied stochastic blockmodel. When the graph is not exceptionally sparse, in particular, when each edge appears with probability omega (n^{-(1+1/r)}), under certain mild assumptions, we prove that the optimal seeding strategy is to put all the seeds in a single community. This matches the intuition that in a nonsubmodular cascade model placing seeds near each other creates synergy. However, it sharply contrasts with the intuition for submodular cascade models (e.g., the independent cascade model and the linear threshold model) in which nearby seeds tend to erode each others' effects. Finally, we show that this observation yields a polynomial time dynamic programming algorithm which outputs optimal seeds if each edge appears with a probability either in omega (n^{-(1+1/r)}) or in o (n^{-2}).

Subject Classification

ACM Subject Classification
  • Theory of computation → Social networks
  • Mathematics of computing → Random graphs
Keywords
  • Nonsubmodular Influence Maximization
  • Bootstrap Percolation
  • Stochastic Blockmodel

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