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arXiv 1602.06236cs.DB
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并行查询处理中的通信开销

Communication Cost in Parallel Query Processing

Paul Beame, Paraschos Koutris, Dan Suciu

摘要:

我们研究了在没有共享存储的并行结构上计算大型数据库上的合取查询问题。使用这种查询$q$的结构和数据中的偏斜,我们研究处理器数量、通信轮数和每个处理器负载(每个处理器在单个轮中可以发送或接收的位数)之间的权衡,这些都是计算$q$所需的。当数据是免费的偏斜,我们得到本质上紧的上界和下界的一轮算法,我们展示了如何降低边界时,有偏斜的数据。在偏斜数据的情况下,我们展示了如何改进算法时,近似程度的重击元素是可用的,获得基本上是最佳的算法,如简单的连接和三角连接查询查询。对于查询,我们确定为树状,我们还证明了几乎匹配的上界和下界的多轮算法的一个自然类的无偏斜数据库。这些后一个下界的一个结果是,对于任何$\varepsilon>0$,使用$p$处理器来计算图的连通分量,或者输出具有$m$边的图的指定顶点对之间的路径(如果有的话),并且每个处理器的负载是$O(m/p^{1-\varepsilon})$,这需要$Ω(\log p)$轮通信。我们的上界由使用MapReduce的简单结构化算法给出。我们的一轮下界证明在一个非常一般的模型,我们称之为大规模并行通信(MPC)模型,允许处理器通信任意位。我们的多轮下限适用于MPC模型的受限版本,其中在第一个通信轮之后的后续轮中的处理器仅允许发送元组。

英文摘要:

We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a query $q$ and the skew in the data, we study tradeoffs between the number of processors, the number of rounds of communication, and the per-processor load -- the number of bits each processor can send or can receive in a single round -- that are required to compute $q$. When the data is free of skew, we obtain essentially tight upper and lower bounds for one round algorithms and we show how the bounds degrade when there is skew in the data. In the case of skewed data, we show how to improve the algorithms when approximate degrees of the heavy-hitter elements are available, obtaining essentially optimal algorithms for queries such as simple joins and triangle join queries. For queries that we identify as tree-like, we also prove nearly matching upper and lower bounds for multi-round algorithms for a natural class of skew-free databases. One consequence of these latter lower bounds is that for any $\varepsilon>0$, using $p$ processors to compute the connected components of a graph, or to output the path, if any, between a specified pair of vertices of a graph with $m$ edges and per-processor load that is $O(m/p^{1-\varepsilon})$ requires $Ω(\log p)$ rounds of communication. Our upper bounds are given by simple structured algorithms using MapReduce. Our one-round lower bounds are proved in a very general model, which we call the Massively Parallel Communication (MPC) model, that allows processors to communicate arbitrary bits. Our multi-round lower bounds apply in a restricted version of the MPC model in which processors in subsequent rounds after the first communication round are only allowed to send tuples.

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