Budget-Independent Influence Maximization in Nearly Linear Time

2026-09-20

AI Summary

本文提出了一种在几乎线性时间内解决独立级联模型中影响力最大化问题的新算法，消除了运行时间对种子预算k的依赖。

Abstract

Influence maximization asks for $k$ seed vertices that maximize the expected spread of a diffusion process in a network. Standard near-optimal-time algorithms based on reverse-reachable sampling achieve a $(1-1/e-\varepsilon)$ approximation, but their worst-case running-time bounds grow linearly with the seed budget $k$. We remove this multiplicative dependence: for the independent cascade model, our algorithm succeeds with probability at least $1-δ$ in $O((m+n)\varepsilon^{-3}\log(2n/δ))$ expected time. The result extends to triggering models with explicitly charged local sampling costs. We reserve $O(\varepsilon k)$ seed positions for cost-weighted random vertices, allowing reverse-reachable searches to stop as soon as they encounter a reserved seed. An independent sample-count estimation phase uses a statistic that also controls the expected search cost. Matching these quantities eliminates the multiplicative dependence on $k$ while preserving the approximation guarantee.

Problem

• influence maximization
• budget-independent
• near-linear time

Innovation

• influence maximization
• near-linear time
• reverse-reachable sampling
• seed budget independence