New selection algorithm based on generating sequences

Abstract

Abstract The paper proposes a new deterministic selection algorithm with computational complexity O(n), called cs-select, which is a modification of the quickselect algorithm. The changes concern the selection of reference elements. Instead of selecting some elements of the sequence itself as References, the cs-select algorithm proposes to use finite segments of complete sequences, that allow to represent any natural number in a given range as the sum of elements from a selected finite segment of the complete sequence. It is theoretically justified that in the cs-select algorithm, the number of comparisons when searching for the k-th statistic in a sequence of length n can converge to the value 2n with unlimited growth of n for some complete sequences. It was also shown that different variations of the complete sequences make it possible to reduce the latent constant in O(n) less than 2.