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arXiv 1306.5972cs.DB
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并行查询处理的通信步骤

Communication Steps for Parallel Query Processing

Paul Beame, Paraschos Koutris, Dan Suciu

摘要:

我们考虑的问题,计算一个关系查询$q$上的大型输入数据库的大小$n$,使用大量的$p$的服务器。计算是按轮执行的,每个服务器只能接收$O(n/p^{1-\varepsilon})$位数据,其中$\varepsilon \in [0,1]$是控制复制的参数。我们研究了计算$q$需要多少全局通信步骤。我们在两种情况下建立下限和上限。对于一个单一的一轮通信,我们给出了最强的可能的模型,任意位可以交换的下界,我们表明,任何算法都需要$\varepsilon \geq 1-1/τ^*$,其中$τ^*$是分数顶点覆盖的超图的$q$。我们还给出了一个算法,匹配的下限为特定类别的数据库。对于多轮通信,我们提出了一个模型中的元组的路由决策是基于元组的下限。我们表明,类树查询轮数和空间指数$\varepsilon$之间存在一个折衷。多轮的下限是同类中的第一个。我们的结果也意味着传递闭包不能在O(1)轮的通信中计算。

英文摘要:

We consider the problem of computing a relational query $q$ on a large input database of size $n$, using a large number $p$ of servers. The computation is performed in rounds, and each server can receive only $O(n/p^{1-\varepsilon})$ bits of data, where $\varepsilon \in [0,1]$ is a parameter that controls replication. We examine how many global communication steps are needed to compute $q$. We establish both lower and upper bounds, in two settings. For a single round of communication, we give lower bounds in the strongest possible model, where arbitrary bits may be exchanged; we show that any algorithm requires $\varepsilon \geq 1-1/τ^*$, where $τ^*$ is the fractional vertex cover of the hypergraph of $q$. We also give an algorithm that matches the lower bound for a specific class of databases. For multiple rounds of communication, we present lower bounds in a model where routing decisions for a tuple are tuple-based. We show that for the class of tree-like queries there exists a tradeoff between the number of rounds and the space exponent $\varepsilon$. The lower bounds for multiple rounds are the first of their kind. Our results also imply that transitive closure cannot be computed in O(1) rounds of communication.

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