Column-Based Partitioning for Data in High Dimensional Space

Several scientific applications such as 3D Jacobi iteration (Rivera and Tseng, 2000) and LQCD (Gupta,1996) demand high computing power, and run on parallel systems. Such applications mostly operate on high dimensional data, and partitioning them into smaller units would help reduce their execution time considerably. Many algorithms such as CBP (Beaumont, 2001), dissect (Nagamochi and Abe, 2003), and bisection (Crandall and Quinn, 1993) are proposed to find an optimal partitioning for two dimensional data. Simply extending such algorithms to handle higher dimensional data does not guarantee the maximum efficiency since the number of data dimensions must be taken into account. In addition, the communication cost among data in high dimensions is increased since data have high interaction to each other. This paper proposes a new algorithm called HyperCBP which is a general optimal column-based partitioning in high dimensional space. The algorithm divides high dimensional data into rectangle blocks of different sizes according to the computing power of each computing node, and minimizes the communication time used in transferring data among rectangles. We evaluate our algorithm using the new defined performance metric called communication saving ratio (CSR). When compared with dissect and bisection, the results show that HyperCBP gives a higher CSR than those two algorithms, and thus results in a better partitioning.