Length of strings for a merge sort
Donald E. Knuth · Communications of the ACM · 1963
Detailed statistics are given on the length of maximal sorted strings which result from the first (internal sort) phase of a merge sort onto tapes. It is shown that the strings produced by an alternating method (i.e. one which produces ascending and descending strings alternately) tend to be only three-fourths as long as those in a method which produces only ascending strings, contrary to statements which have appeared previously in the literature. A slight modification of the read-backward polyphase merge algorithm is therefore suggested.