Parallel Construction and Searches of Digital Trees

Geometric searching is an element of mesh generation, interpolation, visualization, collision detection, and many other tasks. The task is searching a cloud of points for the nearest point to a target or all cloud points within a specified distance from a target. This is inherently a O(N) search problem for each query if all N cloud points points are interrogated. Fortunately, this complexity can be reduced to O(log(N)). This reduction is a product of recursively partitioning the cloud to be searched and narrowing the search to only plausible partitions. This partitioned cloud of points is often stored in an organized structure to facilitate efficient pruning of potential candidates while searching for nearby entities or the nearest entity. Digital trees are a common data structure for this storage. The execution time can be long for a large number of target queries or a large number of cloud points, even for O(log(N)) methods. Parallel algorithms are able to speed up the search process and efficiently address problems that are larger than the main memory of a single processor machine. The goal of this project is compare the performance of different tree varieties and exhaustive search in a parallel setting. There is a large variety of methods for partitioning the search cloud for storage in a tree. These various methods have different strengths and weaknesses. Reference [1] makes comparisons of three such search methods. Reference [2] compares an exhaustive search to a tree search. Parallel algorithms have also been investigated in References [3] and [4].