Given a graph G , a source node s, and a target node t , the personalized PageRank ( PPR ) of t with respect to s is the probability that a random walk starting from s terminates at t . An important variant of the PPR query is single-source PPR ( SSPPR ), which enumerates all nodes in G and returns the top- k nodes with the highest PPR values with respect to a given source s . PPR in general and SSPPR in particular have important applications in web search and social networks, e.g., in Twitter’s Who-To-Follow recommendation service. However, PPR computation is known to be expensive on large graphs and resistant to indexing. Consequently, previous solutions either use heuristics, which do not guarantee result quality, or rely on the strong computing power of modern data centers, which is costly. Motivated by this, we propose effective index-free and index-based algorithms for approximate PPR processing, with rigorous guarantees on result quality. We first present FORA, an approximate SSPPR solution that combines two existing methods—Forward Push (which is fast but does not guarantee quality) and Monte Carlo Random Walk (accurate but slow)—in a simple and yet non-trivial way, leading to both high accuracy and efficiency. Further, FORA includes a simple and effective indexing scheme, as well as a module for top- k selection with high pruning power. Extensive experiments demonstrate that the proposed solutions are orders of magnitude more efficient than their respective competitors. Notably, on a billion-edge Twitter dataset, FORA answers a top-500 approximate SSPPR query within 1s, using a single commodity server.

中文翻译：

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近似单源个性化 PageRank 查询的高效算法

给定一张图G, 一个源节点年代，和一个目标节点吨， 这个性化的PageRank(PPR） 的吨关于s是随机游走从s终止于吨. PPR 查询的一个重要变体是单源 PPR(SSPPR)，它枚举了所有节点G并返回顶部-ķ对于给定源具有最高 PPR 值的节点s. 一般的 PPR 和特别是 SSPPR 在网络搜索和社交网络中具有重要应用，例如，在 Twitter 的 Who-To-Follow 推荐服务中。然而，众所周知，PPR 计算在大图上代价高昂并且难以索引。因此，以前的解决方案要么使用不能保证结果质量的启发式算法，要么依赖现代数据中心的强大计算能力，但成本很高。受此启发，我们提出了有效的无索引和基于索引的近似 PPR 处理算法，并严格保证结果质量。我们首先介绍了 FORA，这是一种近似的 SSPPR 解决方案，它以简单但不平凡的方式结合了两种现有方法——前推（快速但不保证质量）和蒙特卡洛随机游走（准确但缓慢），从而实现高精度和高效率。此外，FORA 包括一个简单有效的索引方案，以及一个用于顶部的模块ķ选择具有高修剪能力。大量实验表明，所提出的解决方案比其各自的竞争对手效率高出几个数量级。值得注意的是，在一个十亿边缘的 Twitter 数据集上，FORA 使用单个商品服务器在 1 秒内回答了前 500 个近似 SSPPR 查询。