Influence maximization (IM) is the problem of finding a seed vertex set which is expected to incur the maximum influence spread on a graph. It has various applications in practice such as devising an effective and efficient approach to disseminate information, news or ad within a social network. The problem is shown to be NP-hard and approximation algorithms with provable quality guarantees exist in the literature. However, these algorithms are computationally expensive even for medium-scaled graphs. Furthermore, graph algorithms usually suffer from spatial and temporal irregularities during memory accesses, and this adds an extra cost on top of the already expensive IM kernels. In this article we leverage fused sampling, memoization, and vectorization to restructure, parallelize and boost their performance on undirected networks. The proposed approach employs a pseudo-random function and performs multiple Monte-Carlo simulations in parallel to exploit the SIMD lanes effectively and efficiently. In addition, it significantly reduces the number of edge traversals, hence the amount of data brought from the memory, which is critical for almost all memory-bound graph kernels. We apply the proposed approach to the traditional MixGreedy algorithm and propose INFuseR-MG which is more than $3000\times$3000× faster than the greedy approaches and can run on large graphs that have been considered as too large in the literature. For instance, the new algorithm runs in 2.09, 0.08, 0.36 seconds on graphs Amazon, NetHEP, NetPhy with 16 threads where the sequential baseline takes 141.3, 259.1 and 1725.2 seconds, respectively. To compare INFuseR-MG with the state-of-the-art approximation algorithms, we conduct a thorough experimental analysis with various influence settings. The results on real-life, undirected networks show that on 16 threads, INFuseR-MG is $2.3\times$2.3×–$173.8\times$173.8× faster than state-of-the-art while being superior in terms of influence scores, and using a comparable amount of memory.

中文翻译：

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使用融合和矢量化提升无向网络的并行影响最大化内核

影响最大化 (IM) 是寻找种子顶点集的问题，该种子顶点集预计会在图上产生最大的影响传播。它在实践中具有多种应用，例如设计一种有效且高效的方法来在社交网络中传播信息、新闻或广告。该问题被证明是 NP-hard 和具有可证明质量保证的近似算法存在于文献中。然而，即使对于中等规模的图，这些算法在计算上也是昂贵的。此外，图算法在内存访问期间通常会遇到空间和时间的不规则性，这在已经很昂贵的 IM 内核之上增加了额外的成本。在本文中，我们利用融合采样、记忆化和矢量化来重构、并行化并提高它们在无向网络上的性能。所提出的方法采用伪随机函数并并行执行多个蒙特卡罗模拟，以有效和高效地利用 SIMD 通道。此外，它显着减少了边遍历的次数，从而减少了从内存中带来的数据量，这对于几乎所有受内存限制的图内核来说都是至关重要的。我们将建议的方法应用于传统的混合贪婪 算法和建议 INFuseR-MG 这比 $3000\次$3000× 比贪婪方法更快，并且可以在被认为是的大图上运行 太大了在文献中。例如，新算法在图形上的运行时间分别为 2.09、0.08、0.36 秒亚马逊, 网络HEP, 网络物理有 16 个线程，其中顺序基线分别需要 141.3、259.1 和 1725.2 秒。比较INFuseR-MG使用最先进的近似算法，我们对各种影响设置进行了彻底的实验分析。在现实生活中的无向网络上的结果表明，在 16 个线程上，INFuseR-MG 是 $2.3\times$2.3×——$173.8\times$173.8× 比最先进的技术更快，同时在影响力得分方面更胜一筹，并使用相当数量的内存。