Maximizing Social Influence in Almost Linear Time

2026-09-28

AI Summary

This study addresses the long-standing computational bottleneck in influence maximization, where algorithmic time complexity has been constrained by a multiplicative dependence on the seed set size $k$, yielding an $O((n+m)k)$ bound that impedes large-scale network applications. By leveraging standard diffusion models alongside novel algorithmic design and efficient data structure optimizations, this work eliminates the multiplicative dependence of the running time on $k$ for the first time. The proposed approach reduces the time complexity to near-linear $O(n+m)$ while preserving the optimal $(1-1/e-\varepsilon)$ approximation guarantee for efficient seed set selection. This contribution resolves a persistent open problem in the field and substantially enhances the computational efficiency of information diffusion modeling in large-scale social networks.

Abstract

Influence maximization is a central algorithmic challenge in network analysis, aiming to identify a set of $k$ seed nodes in a graph with $n$ nodes and $m$ edges that maximizes the expected cascade of information under standard diffusion models. The seminal work of Borgs, Brautbar, Chayes, and Lucier (SODA'14) yielded a fundamental breakthrough\footnote{The conference version of their paper originally claimed a runtime of $\tilde O_ε(n+m)$, but this was subsequently corrected to a runtime of $\tilde O_ε((n+m)k)$ in an updated version of the paper that is available online. We validate the necessity of this additional factor $k$ in Section~\ref{sec:lowerbound} by demonstrating that if their algorithm is restricted to a runtime budget of $\tilde{O}_ε(n+m)$, the approximation ratio deteriorates to $O(k^{-1/4})$.} for this problem by achieving an $\tilde O_ε((n+m)k)$ time algorithm for approximating the solution within a factor of $1-1/e-ε$. In the years since, numerous efforts have attempted to improve the runtime of this algorithm; however, these works have been successful in only shaving logarithmic factors or improving the dependence on $ε$, leaving the existence of an almost linear-time algorithm as an open question. In this work, we resolve this long-standing open question. We present a novel algorithm that approximates the influence maximization problem within a factor of $1-1/e-ε$ in time $\tilde{O}_ε(n+m)$, effectively removing the multiplicative dependence on $k$ from the time complexity.

Problem

• Influence Maximization
• Almost Linear Time
• Social Networks
• Approximation Algorithm
• Diffusion Models

Innovation

• Influence Maximization
• Almost Linear Time
• Approximation Algorithm
• Time Complexity
• Diffusion Models