Algorithms and Complexity of Influence Maximization on Directed Acyclic Graphs

2026-05-30

AI Summary

This study investigates the computational complexity and tractability of the influence maximization problem on directed acyclic graphs (DAGs) under the Independent Cascade (IC) and Linear Threshold (LT) diffusion models. Leveraging dynamic programming, complexity analysis, and approximation algorithm design—combined with structural properties such as the unique-path condition—the work establishes for the first time that the problem remains APX-hard under the LT model even on DAGs. Furthermore, it demonstrates equivalence between the IC and LT models on out-arborescences and provides an exact polynomial-time algorithm for this setting. For the IC model on in-arborescences, the paper presents a fully polynomial-time approximation scheme (FPTAS). These results comprehensively delineate the complexity landscape of influence maximization over restricted tree-like structures, highlighting the critical role of graph topology in determining problem solvability.

Abstract

This paper investigates the influence maximization problem under the Independent Cascade(IC) and Linear Threshold (LT) models. While this problem is known to be APX-hard on general graphs, we explore its computational limits by focusing on Directed Acyclic Graphs (DAGs) and more restricted tree structures. Our primary result demonstrates that influence maximization remains APX-hard on DAGs under the LT model, suggesting that the absence of cycles is insufficient to achieve a polynomial-time approximation scheme (PTAS). In contrast, we show that the problem becomes tractable when the topology is further restricted to out-arborescences and in-arborescences. Specifically, for out-arborescences, we show that the IC model and the LT model are equivalent, and we develop exact polynomial-time algorithms based on dynamic programming that leverage the unique path properties of these structures. For in-arborescences, it is known that the problem is polynomial-time solvable under the LT model, and it is NP-hard under the IC model. We complement these results by presenting a fully polynomial-time approximation scheme (FPTAS) for the IC model.

Problem

• Influence Maximization
• Directed Acyclic Graphs
• Computational Complexity
• Independent Cascade Model
• Linear Threshold Model

Innovation

• influence maximization
• Directed Acyclic Graphs
• APX-hardness
• arborescence
• FPTAS