AI 中文总结
本研究提出一种几乎线性时间算法，在Õ_ε(n+m)时间内以1-1/e-ε近似因子解决影响力最大化问题，消除了对k的依赖，解决了长期开放问题。
AI 中文摘要
影响力最大化是网络分析中的一个核心算法挑战，旨在识别具有n个节点和m条边的图中一组k个种子节点，以在标准扩散模型下最大化信息的预期级联。Borgs、Brautbar、Chayes和Lucier（SODA'14）的开创性工作为这个问题带来了根本性突破，通过实现一个近似解在因子1-1/e-ε内的Õ_ε((n+m)k)时间算法。自那以后，许多努力试图改进该算法的运行时间；然而，这些工作仅成功削减了对数因子或改善了对ε的依赖，使得几乎线性时间算法的存在性成为一个开放问题。在这项工作中，我们解决了这个长期存在的开放问题。我们提出了一种新颖的算法，在Õ_ε(n+m)时间内近似影响力最大化问题，因子为1-1/e-ε，有效去除了时间复杂度中对k的乘法依赖。
英文摘要
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.
