An analysis of the generalized binary GCD algorithm (2007)
| Venue: | HIGH PRIMES AND MISDEMEANORS, LECTURES IN HONOUR OF HUGH COWIE |
| Citations: | 3 - 1 self |
BibTeX
@INPROCEEDINGS{Sorenson07ananalysis,
author = {Jonathan P. Sorenson},
title = {An analysis of the generalized binary GCD algorithm },
booktitle = {HIGH PRIMES AND MISDEMEANORS, LECTURES IN HONOUR OF HUGH COWIE},
year = {2007},
pages = {247--252},
publisher = {}
}
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OpenURL
Abstract
In this paper we analyze a slight modification of Jebelean’s version of the k-ary GCD algorithm. Jebelean had shown that on n-bit inputs, the algorithm runs in O(n²) time. In this paper, we show that the average running time of our modified algorithm is O(n²/ log n). This analysis involves exploring the behavior of spurious factors introduced during the main loop of the algorithm. We also introduce a Jebeleanstyle left-shift k-ary GCD algorithm with a similar complexity that performs well in practice.
