On computing an optimal permutation of ranks for multiselection

Authors:
M. H. Alsuwaiyel
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Given a set of n elements, and a sorted sequence K=k"1,k"2,...,k"r of positive integers between 1 and n, it is required to find the k"ith smallest element for all values of i,1@?i@?r. We present a dynamic programming algorithm for computing an optimal permutation of the input ranks that results in the least number of comparisons when used as a preprocessing step with any algorithm that uses repetitive calls to an algorithm for selection. The running time of the proposed algorithm is O(r^3).