Linear-Time Exact Computation of Influence Spread on Bounded-Pathwidth Graphs

2026-04-15

AI Summary

Under the independent cascade model, exactly computing the influence spread of seed nodes in directed uncertain graphs is #P-hard. This work proposes a dynamic programming approach based on the graph’s pathwidth that achieves exact computation in linear time by identifying and reusing recurring substructures. Specifically, the proposed method reduces the time complexity from the previous $O(mn\omega_p^2 \cdot 2^{\omega_p^2})$ to $O((m+n)\omega_p^2 \cdot 2^{\omega_p^2})$, where $m$ and $n$ denote the numbers of edges and vertices, respectively, and $\omega_p$ is the pathwidth of the underlying graph. This substantial improvement in computational efficiency provides a practical exact solution for influence analysis on large-scale uncertain graphs.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Given a network and a set of vertices called seeds to initially inject information, influence spread is the expected number of vertices that eventually receive the information under a certain stochastic model of information propagation. Under the commonly used independent cascade model, influence spread is equivalent to the expected number of vertices reachable from the seeds on a directed uncertain graph, and the exact evaluation of influence spread offers many applications, e.g., influence maximization. Although its evaluation is a \#P-hard task, there is an algorithm that can precisely compute the influence spread in $O(mnω_p^2\cdot 2^{ω_p^2})$ time, where $ω_p$ is the pathwidth of the graph. We improve this by developing an algorithm that computes the influence spread in $O((m+n)ω_p^2\cdot 2^{ω_p^2})$ time. This is achieved by identifying the similarities in the repetitive computations in the existing algorithm and sharing them to reduce computation. Although similar refinements have been considered for the probability computation on undirected uncertain graphs, a greater number of similarities must be leveraged for directed graphs to achieve linear time complexity.

Problem

• influence spread
• bounded-pathwidth graphs
• independent cascade model
• exact computation
• directed uncertain graphs

Innovation

• influence spread
• bounded-pathwidth graphs
• linear-time algorithm
• directed uncertain graphs
• independent cascade model