发表机构
Fuzhou University（福州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对影响力最大化问题，提出一种预算无关的算法，通过保留种子位置和样本计数估计，在近乎线性时间内达到 $(1-1/e-\varepsilon)$ 近似，消除了对种子预算 $k$ 的乘法依赖。
AI 中文摘要
影响力最大化问题要求选择 $k$ 个种子顶点，以最大化网络中扩散过程的期望传播范围。基于反向可达采样的标准近最优时间算法实现了 $(1-1/e-\varepsilon)$ 近似比，但其最坏情况运行时间界限随种子预算 $k$ 线性增长。我们消除了这种乘法依赖：对于独立级联模型，我们的算法在 $O((m+n)\varepsilon^{-3}\log(2n/\delta))$ 期望时间内以至少 $1-\delta$ 的概率成功。该结果扩展到具有显式计费局部采样成本的触发模型。我们为成本加权随机顶点保留 $O(\varepsilon k)$ 个种子位置，允许反向可达搜索在遇到保留种子时立即停止。一个独立的样本计数估计阶段使用一个统计量，该统计量同时控制期望搜索成本。匹配这些量消除了对 $k$ 的乘法依赖，同时保持了近似保证。
英文摘要
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 expected 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.
