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- W2029744427 abstract "Given a complete k -partite graph G = ( V 1 , V 2 , … , V k ; E ) satisfying | V 1 | = | V 2 | = ⋯ = | V k | = n and weights of all k -cliques of G , the k -dimensional assignment problem finds a partition of vertices of G into a set of (pairwise disjoint) n k -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 G are embedded in the d -dimensional space Q d 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. We propose a second-order cone programming relaxation of the problem and a polynomial time randomized rounding procedure. We show that the expected objective value obtained by our algorithm is bounded by ( 5 / 2 − 3 / k ) times the optimal value. Our result improves the previously known bound ( 4 − 6 / k ) of the approximation ratio." @default.
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- W2029744427 date "2009-05-01" @default.
- W2029744427 modified "2023-10-02" @default.
- W2029744427 title "An approximation algorithm for multidimensional assignment problems minimizing the sum of squared errors" @default.
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- W2029744427 doi "https://doi.org/10.1016/j.dam.2007.10.013" @default.
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