基于MapReduce的C-Cubing并行算法

封闭立方体计算的主要任务是在生成一个数据单元时，判断其是否封闭。针对该问题，C-Cubing是新近提出的一种有效的方法，不同以往基于输出或基于元组的方法，它仅通过特定的度量，即封闭性度量，就可以判断出封闭单元。然而随着数据量的增加，C-Cubing的性能下降，因此它的并行算法还有待研究。本文提出基于MapReduce并行框架，采用C-Cubing对封闭立方体并行计算的方法，并在Hadoop上给予了实现。实验结果表明，本方案能够利用廉价的PC机器，有效提高了在较大数据集上计算封闭立方体的性能。

A parallel C-Cubing algorithm based on MapReduce

The main task of closed cubes computation is to check the closeness of a new data cell. To address this issue, C-Cubing is an efficient approach recently proposed. Unlike the previous output-based and tuple-based method, it checks the closeness only by the closeness measure. However, with the size of data sets increasing, the performance of C-Cubing becomes worse, so the parallel C-Cubing algorithm needs to be studied. This paper presents a solution where C-Cubing is parallelized based on the MapReduce framework. We give an implementation using Hadoop. The experiments show that by employing low cost PC machines, our solution efficiently improves the performance for computing the closed cube on large data sets.