k-way merging and k-ary sorts

We present a divide-and-conquer algorithm for merging k sorted lists, namely, recursively merge the first lists, do likewise for the last lists, then merge the two results. We get a tight bound for the expense, in comparisons made between list elements, of this merge. We show the algorithm is cheapest among all similar divide-and-conquer approaches to k-way merging. We compute the expense of the k-ary sort, which, in analogy to the binary sort, divides its input list into k sublists. Sometimes the k-ary sort has the same expense as the binary sort. Finally we briefly consider parallelizing these algorithms.