Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using n log n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using n log n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a n log n processor PRAM, butterfly, or tree. Keywords. Hierarchical clustering, pattern analysis, parallel algorithm, butterfly network, PRAM algorithm. 1 In...

INTRODUCTION Despite recent advances in computer vision the recognition and localization of 3D objects from a 2D image of a cluttered scene is still a key problem. The reason for the difficulty to progress mainly lies in the combinatorial aspect of the problem. This difficulty can be bypassed if the location of the objects in the image is known. In that case, the problem is to compare efficiently a region of the image to a viewer-centered object database. (See Fig. 1 for the figures used in our experiments.) Recent proposed solutions are, for example, based on principal component analysis [1, 2], modal matching [3], or template matching [4]. But Grimson [5] emphasized that the hard part of the recognition problem is in separating out subsets of correct data from the spurious data that arise from a single object. Recent researchesinthisfieldhave focused on the various components of the recognition problem: which features are invariant and discriminant [6], how it is possible