Polystore mathematics of relational algebra
Polystore mathematics of relational algebra
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DOI：
10.1109/bigdata.2017.8258298
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
Hayden Jananthan;Ziqi Zhou;V. Gadepally;D. Hutchison;Suna Kim;J. Kepner
中科院分区：
文献类型：
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作者：
Hayden Jananthan;Ziqi Zhou;V. Gadepally;D. Hutchison;Suna Kim;J. Kepner
金融交易、互联网搜索和数据分析都对数据库提出了越来越高的要求。SQL、NoSQL和NewSQL数据库都是为了满足这些需求而开发的，每种数据库都提供了独特的优势。SQL、NoSQL和NewSQL数据库也依赖于不同的底层数学模型。Polystores试图提供一种机制，允许应用程序透明地实现不同数据库的好处，同时将应用程序与这些数据库的细节隔离开来。集成这些不同数据库的基础数学可以成为polystores的重要推动因素，因为它可以在不同数据库之间进行有效推理。关联数组通过包含不同数据库中的数学，为polystore的数学提供了一种通用方法：集合（SQL），图形（NoSQL）和矩阵（NewSQL）。以前的工作提出了SQL关系模型的关联数组和确定的关键数学属性，保留在SQL中。这项工作提供了严格的数学定义，引理，这些性质的基础定理。具体来说，SQL关系代数主要处理关系-元组的多集-以及这些关系上和关系之间的操作。通过将元组视为数组中的非零行，可以将这些关系建模为关联数组。关系代数中的操作是由关联数组上的标准操作组成的，这些标准操作反映了它们的矩阵对应物。这些构造提供了如何通过数组操作处理关系代数的见解。作为示例应用，两个投影操作的组合被示出为也是投影，并且并集的投影被示出为等于投影的并集。
Financial transactions, internet search, and data analysis are all placing increasing demands on databases. SQL, NoSQL, and NewSQL databases have been developed to meet these demands and each offers unique benefits. SQL, NoSQL, and NewSQL databases also rely on different underlying mathematical models. Polystores seek to provide a mechanism to allow applications to transparently achieve the benefits of diverse databases while insulating applications from the details of these databases. Integrating the underlying mathematics of these diverse databases can be an important enabler for polystores as it enables effective reasoning across different databases. Associative arrays provide a common approach for the mathematics of polystores by encompassing the mathematics found in different databases: sets (SQL), graphs (NoSQL), and matrices (NewSQL). Prior work presented the SQL relational model in terms of associative arrays and identified key mathematical properties that are preserved within SQL. This work provides the rigorous mathematical definitions, lemmas, and theorems underlying these properties. Specifically, SQL Relational Algebra deals primarily with relations — multisets of tuples — and operations on and between those relations. These relations can be modeled as associative arrays by treating tuples as non-zero rows in an array. Operations in relational algebra are built as compositions of standard operations on associative arrays which mirror their matrix counterparts. These constructions provide insight into how relational algebra can be handled via array operations. As an example application, the composition of two projection operations is shown to also be a projection, and the projection of a union is shown to be equal to the union of the projections.