Samuel W. Reynolds
Abstract
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.
- 1 MILES, E. P., JR. Generalized Fibonacci numbers and associated matrices. Amer. Math. Month. 67 (Oct. 1960), 745-752.Google Scholar
Cross Ref
- 2 FLORES, IVAN. Analysis of internal computer sorting. J. ACM 8 (Jan. 1961), 41-80. Google ScholarDigital Library
- 3 GILSTAD, R. L. Polyphase merge sorting-an advanced technique. Proc. Eastern Joint Comp. Conf., Dec. 1960.Google Scholar
- 4 BETZ, B. K. New merge sorting techniques. ACM Conf., Sept. 1959. Google ScholarDigital Library
Index Terms
- A generalized polyphase merge algorithm
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