An efficient selection algorithm on the pyramid

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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 x1, x2, …, xN where a non-negative weight wi is assigned to each element xi for all i so that ∑i = 1Nwi = W. The algorithm has a time complexity of O((NW)ε) using N processors for some ε lying between 0 and 1. When w1 = w2 = … = wN = 1, the problem reduces to that of finding the kth largest element out of N elements. In that case the algorithm has a time complexity of O(Nε) and a cost of O(N1 + ε), for some ε lying between 0 and 1.

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