Abstract
This paper presents a generalized selection algorithm on a two-dimensional pyramid model. The algorithm finds the weighted quantile of order f out of N elements x 1 , x 2 , …, x N where a non-negative weight w i is assigned to each element x i for all i so that ∑ i = 1 N w i = W . The algorithm has a time complexity of O(( NW ) ε ) using N processors for some ε lying between 0 and 1. When w 1 = w 2 = … = w N = 1, the problem reduces to that of finding the k th largest element out of N elements. In that case the algorithm has a time complexity of O( N ε ) and a cost of O( N 1 + ε ), for some ε lying between 0 and 1.
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