Optimal Polyphase Sorting

A read-forward polyphase merge algorithm is described which performs the polyphase merge starting from an arbitrary string distribution. This algorithm minimizes the volume of information moved. Since this volume is easily computed, it is possible to construct dispersion algorithms which anticipate the merge algorithm. Two such dispersion techniques are described. The first algorithm requires that the number of strings to be dispersed be known in advance; this algorithm is optimal. The second algorithm makes no such requirement, but is not always optimal. In addition, performance estimates are derived and both algorithms are shown to be asymptotically optimal.