无向图上的影响最大化:接近(1-1/e)差距

G. Schoenebeck, Biaoshuai Tao
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引用次数: 9

摘要

我们研究了无向网络中的影响最大化问题,特别关注了独立级联模型和线性阈值模型。我们证明了两种模型的apx -硬度(对于某些常数τ>0$,在因子(1-τ)内近似的np -硬度),改进了线性阈值模型的np -硬度下界。以前没有已知的独立级联模型的硬度结果。作为硬度证明的一部分,我们展示了这些级联在无向图上的一些自然性质。例如,我们证明了在线性阈值模型和独立级联模型的一种特殊情况(称为加权独立级联模型)中,种子集S的期望感染数是由S的切边大小上界的。在上界的激励下,我们提出了一套高度可扩展的局部贪婪启发式算法来解决无向图上线性阈值模型和加权独立级联模型的影响最大化问题,在实践中,我们找到的种子集平均获得了线性阈值模型中慢得多的贪婪算法的97.52%的性能,以及加权独立级联模型中贪婪算法的97.39%的性能。我们的启发式算法也优于其他流行的本地启发式算法,比如Chen等人的学位折扣启发式算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Influence Maximization on Undirected Graphs: Towards Closing the (1-1/e) Gap
We study the influence maximization problem in undirected networks, specifically focusing on the independent cascade and linear threshold models. We prove APX-hardness (NP-hardness of approximation within factor (1-τ) for some constant τ>0$) for both models, which improves the previous NP-hardness lower bound for the linear threshold model. No previous hardness result was known for the independent cascade model. As part of the hardness proof, we show some natural properties of these cascades on undirected graphs. For example, we show that the expected number of infections of a seed set S is upper-bounded by the size of the edge cut of S in the linear threshold model and a special case of the independent cascade model called the weighted independent cascade model. Motivated by our upper bounds, we present a suite of highly scalable local greedy heuristics for the influence maximization problem on both the linear threshold model and the weighted independent cascade model on undirected graphs that, in practice, find seed sets which on average obtain 97.52% of the performance of the much slower greedy algorithm for the linear threshold model, and 97.39% of the performance of the greedy algorithm for the weighted independent cascade model. Our heuristics also outperform other popular local heuristics, such as the degree discount heuristic by Chen et al.
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