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

TL;DR

This paper presents a linear-time algorithm for exactly computing influence spread on bounded-pathwidth graphs, significantly improving previous methods by optimizing repetitive computations.

Contribution

The authors develop a new algorithm that reduces influence spread computation time from superlinear to linear in graph size for bounded-pathwidth graphs.

Findings

The new algorithm computes influence spread in O((m+n)ω_p^2 2^{ω_p^2}) time.

It shares repetitive computations to achieve linear time complexity.

The approach is tailored for directed graphs with bounded pathwidth.

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 $O(mn\omega_p^2\cdot 2^{\omega_p^2})$ time, where $\omega_p$ is the pathwidth of the graph. We improve this by developing an algorithm that computes the influence spread in $O((m+n)\omega_p^2\cdot 2^{\omega_p^2})$ 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.