Abstract
A sort sequence $S_n$ is a sequence of all unordered pairs of indices in $I_n\;=\;{1,\;2,v...,\;n}$. With a sort sequence Sn we assicuate a sorting algorithm ($AS_n$) to sort input set $X\;=\;{x_1,\;x_2,\;...,\;x_n}$ as follows. An execution of the algorithm performs pairwise comparisons of elements in the input set X as defined by the sort sequence $S_n$, except that the comparisons whose outcomes can be inferred from the outcomes of the previous comparisons are not performed. Let $X(S_n)$ denote the acverage number of comparisons required by the algorithm $AS_n$ assuming all input orderings are equally likely. Let $X^{\ast}(n)\;and\;X^{\circ}(n)$ denote the minimum and maximum value respectively of $X(S_n)$ over all sort sequences $S_n$. Exact determination of $X^{\ast}(n),\;X^{\circ}(n)$ and associated extremal sort sequenes seems difficult. Here, we obtain bounds on $X^{\ast}(n)\;and\;X^{\circ}(n)$.