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Maximizing influence in networks is a widely studied problem with applications across various domains. In this paper, we approach this problem by considering influence maximization in directed tree structures. Given a tree T, each node is associated with a binary label, obtaining \(1-\) nodes and \(0-\) nodes. The influence of \(1-\) nodes over T is then computed as the total number of \(0-\) nodes in their neighbourhood. Given an integer k, our objective is to identify a subset of k \(1-\) nodes that maximizes the influence over T. After analysing heuristic approaches and their limitations, we present a dynamic programming algorithm for solving this problem exactly when the maximum degree and k are fixed. Our findings provide new insights into influence maximization in directed tree structures and establish a foundation for further exploration of constrained optimization problems.

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On the Constrained Maximization of Influence Over a Directed Tree Structure

  • 会议论文

  • 发表日期：

    2026年

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  • Niccolò Di Marco,
  • Andrea Frosini,
  • Shinichi Nakano

摘要

Maximizing influence in networks is a widely studied problem with applications across various domains. In this paper, we approach this problem by considering influence maximization in directed tree structures. Given a tree T, each node is associated with a binary label, obtaining \(1-\) nodes and \(0-\) nodes. The influence of \(1-\) nodes over T is then computed as the total number of \(0-\) nodes in their neighbourhood. Given an integer k, our objective is to identify a subset of k \(1-\) nodes that maximizes the influence over T. After analysing heuristic approaches and their limitations, we present a dynamic programming algorithm for solving this problem exactly when the maximum degree and k are fixed. Our findings provide new insights into influence maximization in directed tree structures and establish a foundation for further exploration of constrained optimization problems.