Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube such that each cell contains one or more measures that can be aggregated along dimensions. In a “Big Data” scenario, traditional data warehousing and OLAP operations are clearly not sufficient to address current data analysis requirements, for example, social network analysis. Furthermore, OLAP operations and models can expand the possibilities of graph analysis beyond the traditional graph-based computation. Nevertheless, there is not much work on the problem of taking OLAP analysis to the graph data model. This paper proposes a formal multidimensional model for graph analysis, that considers the basic graph data, and also background information in the form of dimension hierarchies. The graphs in this model are node- and edge-labelled directed multi-hypergraphs, called graphoids, which can be defined at several different levels of granularity using the dimensions associated with them. Operations analogous to the ones used in typical OLAP over cubes are defined over graphoids. The paper presents a formal definition of the graphoid model for OLAP, proves that the typical OLAP operations on cubes can be expressed over the graphoid model, and shows that the classic data cube model is a particular case of the graphoid data model. Finally, a case study supports the claim that, for many kinds of OLAP-like analysis on graphs, the graphoid model works better than the typical relational OLAP alternative, and for the classic OLAP queries, it remains competitive.

中文翻译：

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图形数据的在线分析处理

在线分析处理（OLAP）包括允许查询多维数据库的工具和算法。它基于多维模型，在多维模型中，数据可以看作是一个多维数据集，这样每个单元格都包含一个或多个可以沿维度聚合的度量。在“大数据”场景中，传统的数据仓库和OLAP操作显然不足以满足当前的数据分析要求，例如社交网络分析。此外，OLAP操作和模型可以将图形分析的可能性扩展到传统的基于图形的计算之外。但是，在将OLAP分析应用于图形数据模型的问题上，尚无太多工作要做。本文提出了一种用于图形分析的正式多维模型，其中考虑了基本图形数据，以及维度层次结构形式的背景信息。该模型中的图形是节点和边缘标记的有向多重图，称为石墨图，可以使用与之相关的尺寸在几个不同的粒度级别上进行定义。类似于普通OLAP多维数据集上使用的操作的定义是基于石墨的。本文提出了针对OLAP的图形模型的正式定义，证明了可以在图形模型上表达对多维数据集的典型OLAP操作，并表明经典数据立方体模型是图形数据模型的特殊情况。最后，一个案例研究支持这样一种说法，即对于图形上的许多类似于OLAP的分析，graphoid模型比典型的关系OLAP替代方案更好，并且对于经典的OLAP查询，它仍然具有竞争力。