An approximation algorithm for multidimensional assignment problems minimizing the sum of squared errors Original Research Article

Given a complete image-partite graph image satisfying image and weights of all image-cliques of image, the image-dimensional assignment problem finds a partition of vertices of image into a set of (pairwise disjoint) image image-cliques that minimizes the sum total of weights of the chosen cliques. In this paper, we consider a case in which the weight of a clique is defined by the sum of given weights of edges induced by the clique. Additionally, we assume that vertices of image are embedded in the image-dimensional space image and a weight of an edge is defined by the square of the Euclidean distance between its two endpoints. We describe that these problem instances arise from a multidimensional Gaussian model of a data-association problem.