A sort sequenceS n is a sequence of all unordered pairs of indices inI n = 1, 2, ...,n. With a sort sequenceS n, we associate a sorting algorithmA(S n) to sort input setX = x 1, x2, ..., xn as follows. An execution of the algorithm performs pairwise comparisons of elements in the input setX as defined by the sort sequenceS n, except that the comparisons whose outcomes can be inferred from the outcomes of the previous comparisons are not performed. Let χ(S n) denote the average number of comparisons required by the algorithmA(S n assuming all input orderings are equally likely. Let χ*(n) and χ∘(n) denote the minimum and maximum values, respectively, of χ(S n) over all sort sequencesS n. Exact determination of χ*(n), χO(n) and associated extremal sort sequences seems difficult. Here, we obtain bounds on χ*(n) and χO(n).
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Yun, M. The characterization of sort sequences. Korean J. Comp. & Appl. Math. 4, 453–467 (1997). https://doi.org/10.1007/BF03014492
AMS Mathematics Subject Classification
Key words and phrases
- graph theory
- optimal sort sequences