Scalable Data Cube Analysis over Big Data

Data cubes are widely used as a powerful tool to provide multidimensional views in data warehousing and On-Line Analytical Processing (OLAP). However, with increasing data sizes, it is becoming computationally expensive to perform data cube analysis. The problem is exacerbated by the demand of supporting more complicated aggregate functions (e.g. CORRELATION, Statistical Analysis) as well as supporting frequent view updates in data cubes. This calls for new scalable and efficient data cube analysis systems. In this paper, we introduce HaCube, an extension of MapReduce, designed for efficient parallel data cube analysis on large-scale data by taking advantages from both MapReduce (in terms of scalability) and parallel DBMS (in terms of efficiency). We also provide a general data cube materialization algorithm which is able to facilitate the features in MapReduce-like systems towards an efficient data cube computation. Furthermore, we demonstrate how HaCube supports view maintenance through either incremental computation (e.g. used for SUM or COUNT) or recomputation (e.g. used for MEDIAN or CORRELATION). We implement HaCube by extending Hadoop and evaluate it based on the TPC-D benchmark over billions of tuples on a cluster with over 320 cores. The experimental results demonstrate the efficiency, scalability and practicality of HaCube for cube analysis over a large amount of data in a distributed environment

Computing Marginals Using MapReduce

We consider the problem of computing the data-cube marginals of a fixed order $k$ (i.e., all marginals that aggregate over $k$ dimensions), using a single round of MapReduce. The focus is on the relationship between the reducer size (number of inputs allowed at a single reducer) and the replication rate (number of reducers to which an input is sent). We show that the replication rate is minimized when the reducers receive all the inputs necessary to compute one marginal of higher order. That observation lets us view the problem as one of covering sets of $k$ dimensions with sets of a larger size $m$, a problem that has been studied under the name "covering numbers." We offer a number of constructions that, for different values of $k$ and $m$ meet or come close to yielding the minimum possible replication rate for a given reducer size