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Influence Maximization in Ising Models

Authors Zongchen Chen, Elchanan Mossel

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Zongchen Chen
  • Department of Computer Science and Engineering, University at Buffalo, NY, USA
Elchanan Mossel
  • Department of Mathematics, MIT, Cambridge, MA, USA

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Zongchen Chen and Elchanan Mossel. Influence Maximization in Ising Models. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Given a complex high-dimensional distribution over {± 1}ⁿ, what is the best way to increase the expected number of +1’s by controlling the values of only a small number of variables? Such a problem is known as influence maximization and has been widely studied in social networks, biology, and computer science. In this paper, we consider influence maximization on the Ising model which is a prototypical example of undirected graphical models and has wide applications in many real-world problems. We establish a sharp computational phase transition for influence maximization on sparse Ising models under a bounded budget: In the high-temperature regime, we give a linear-time algorithm for finding a small subset of variables and their values which achieve nearly optimal influence; In the low-temperature regime, we show that the influence maximization problem cannot be solved in polynomial time under commonly-believed complexity assumption. The critical temperature coincides with the tree uniqueness/non-uniqueness threshold for Ising models which is also a critical point for other computational problems including approximate sampling and counting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Theory of computation → Randomness, geometry and discrete structures
  • Mathematics of computing → Markov networks
  • Mathematics of computing → Probabilistic inference problems
  • Influence maximization
  • Ising model
  • phase transition
  • correlation decay


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