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arXiv · 2609.23604

Budget-Independent Influence Maximization in Nearly Linear Time

Zhijie Zhang
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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.

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Zhijie Zhang. 2026-09-20. Budget-Independent Influence Maximization in Nearly Linear Time. https://arxiv.org/abs/2609.23604

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