Analysis of Internal Computer Sorting
Journal of the ACM (JACM)
ACM '59 Preprints of papers presented at the 14th national meeting of the Association for Computing Machinery
ACM Computing Surveys (CSUR)
Communications of the ACM
Communications of the ACM
String distribution for the polyphase sort
Communications of the ACM
A dispersion pass algorithm for the polyphase merge
Communications of the ACM
Merge-sort analysis by matrix techniques
IBM Systems Journal
| Hi-index | 48.28 |
The k-generalized Fibonacci numbers are defined as in [1]. A polyphase merge (merging an equal number of sequences from k tapes onto a single unused tape) using k+1 tapes is defined in terms of linear combinations of these numbers. A method is described to output sequences onto k of k+1 tapes after the internal sorting of elements to form sequences. This method will permit a polyphase merge of sequences of sorted elements provided that enough sequences are generated internally to place the proper numbers of sequences on each of the k tapes. For each value of k, there is a set of permissible numbers that can represent the total number of sequences generated during the original output process. If one of these numbers is met exactly and if there is a specific distribution of sequences on the k tapes, then a polyphase merge may proceed. If these conditions are not met, an algorithm is necessary to adjust the numbers of sequences to permit a polyphase merge. This paper describes such an algorithm.