We study parallel solutions to the problem of weighted multiselection to select r elements on given weighted-ranks from a set S of n weighted elements, where an element is on weighted rank k if it is the smallest element such that the aggregated weight of all elements not greater than it in S is not smaller than k. We propose efficient algorithms on two of the most popular parallel architectures, hypercube and mesh. For a hypercube with p < n processors, we present a parallel algorithm running

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... n O(n min{r, log p}) time for p = n 1− , 0 < < 1, which is cost optimal when r ≥ p. Our algorithm on √ p × √ p mesh runs in O( √ p + n p log 3 p) time which is the same as multiselection on mesh when r ≥ log p, and thus has the same optimality as multiselection in this case.