EUCLID'S GCD ALGORITHM IS NOT OPTIMAL PART I. UPPER BOUND
| dc.contributor.author | Bshouty, Nader H. | eng |
| dc.date.accessioned | 2008-02-27T16:48:54Z | |
| dc.date.available | 2008-02-27T16:48:54Z | |
| dc.date.computerscience | 1999-05-27 | eng |
| dc.date.issued | 1991-05-01 | eng |
| dc.description.abstract | Using linear arithmetic operations, the floor operation, and indirect addressing, we sequentially compute $GCD(x,y)$ for $0~<=~x,y~<=~N$, and find two integers $-N~<=~a,b~<=~N$ such that $ax~+~by~=~GCD(x,y)$ with operation complexity 0 left ( {log~N} over {log~log~N} right ) and space complexity $0(($log$~N) sup epsilon )$ for any constant $0~<~epsilon~<~1$. The intermediate numbers obtained during the execution of these algorithms are all less than $max(x,y)$. In the second part of this paper (Part II. Lower Bound), we prove that, using the given operations, this bound is tight. We also study the direct sum complexity of computing the GCD and also the complexity of computing the GCD using tables of bounded size. | eng |
| dc.description.notes | We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.ca | eng |
| dc.identifier.department | 1991-430-14 | eng |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/30476 | |
| dc.identifier.uri | http://hdl.handle.net/1880/45741 | |
| dc.language.iso | Eng | eng |
| dc.publisher.corporate | University of Calgary | eng |
| dc.publisher.faculty | Science | eng |
| dc.subject | Computer Science | eng |
| dc.title | EUCLID'S GCD ALGORITHM IS NOT OPTIMAL PART I. UPPER BOUND | eng |
| dc.type | unknown | |
| thesis.degree.discipline | Computer Science | eng |