Optimal Gap Sequences in Shellsort for n≤16 Elements

12/21/2021

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by   Ying Wai Lee, et al.

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Optimal gap sequences in Shellsort, defined as gap sequences having the minimised maximum number of comparisons for a fixed number of pairwise distinct elements, are found by minimax search in reduced permutational spaces, namely Bad (s,1)-sorted permutations. Exact optimal gap sequences in Shellsort for n≤16 pairwise distinct elements are established, and the best known gap sequences for 17≤ n≤ 30 are listed with conjectures made. It notably discovers some optimal gap sequences consist of increments larger than the half of the total number of the elements to sort.