David E. Ferguson

A fixed buffer allocation for merge-sorting is presented here which minimizes the number of input-output operations for a given order of merge. When sorting on movable arm disks, the number of seeks is equal to the number of input-output operations, and the seek time usually controls the sort time. First some standard terminology is introduced. Then the input buffer allocation method is described, followed by an analysis of the improvement to be expected over more conventional allocation. This analysis makes use of a particular distribution function. An analysis of a completely different distribution is given which yields similar results. This suggests that the results do not depend on a particular distribution function. An optimum output buffer size is also determined. It is concluded that this buffering allocation can significantly reduce the time of merge sorting on movable arm disks when the input data are not random, and that this output buffer allocation should be used whether the data is random or not.