Read-backward polyphase sorting
Communications of the ACM
A generalized polyphase merge algorithm
Communications of the ACM
A dispersion pass algorithm for the polyphase merge
Communications of the ACM
A Theorem in the Theory of Compromise Merge Methods
Journal of the ACM (JACM)
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Previous work, which analyzed certain merge-sorting methods with the aid of difference equations, is extended to include a wider range of methods. Matrices are introduced to represent the set or sets of difference equations associated with a merge-sort. Two or more matrices are required to define a Class II method, whereas a Class I method can be defined with one matrix. The merge-sorts of most interest fall into a special subclass called Class Ia. It is shown that an asymptotic solution to the set of diflerence equations for a Class Ia merge-sort is readily obtainable. Carter's analysis of cascade and polyphase merge-sorts is generalized and extended to include, among other things, the compromise merges. Various properties of the Class Ia merge-sorts, including relative performance measures and explicit merge patterns, are shown to be obtainable by matrix multiplication. Although the analysis emphasizes Class Ia merges, suggestions are given for applying the matrix technique to other merge-sorts of Classes I and II.