Letters to the editor: three letters on merging
Communications of the ACM
Merge-sort analysis by matrix techniques
IBM Systems Journal
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Let r be the total number of cycles required to complete a compromise merge of a given number of initial strings. Define row vectors mr-j and dj whose components represent the number and length respectively of strings at the end of the jth cycle of the merge. It is shown in this paper that there are asymptotic approximations to these vectors, which enables one to compute their respective components directly. Consequently, the number of cycles r can be computed directly, as in the case of the balanced merge.