A k-d tree-based algorithm to parallelize Kriging interpolation of big spatial data

Abstract

Parallel computing provides a promising solution to accelerate complicated spatial data processing, which has recently become increasingly computationally intense. Partitioning a big dataset into workload-balanced child data groups remains a challenge, particularly for unevenly distributed spatial data. This study proposed an algorithm based on the k-d tree method to tackle this challenge. The algorithm constructed trees based on the distribution variance of spatial data. The number of final sub-trees, unlike the conventional k-d tree method, is not always a power of two. Furthermore, the number of nodes on the left and right sub-trees is always no more than one to ensure a balanced workload. Experiments show that our algorithm is able to partition big datasets efficiently and evenly into equally sized child data groups. Speed-up ratios show that parallel interpolation can save up to 70% of the execution time of the consequential interpolation. A high efficiency of parallel computing was achieved when the datasets were divided into an optimal number of child data groups.