Fully normal algorithms for incomplete hypercubes

V.K. Prabhala, N.A. Sherwani
[1991] Proceedings. The Fifth International Parallel Processing Symposium  
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALGORITHM S FO R IN CO M PLETE HYPERCUBES V enkata K. Prabhala, M.S. W estern Michigan University, 1992 Networked multiprocessing architectures for parallel com putation offer an alternative to high cost supercom puting. Recently hypercube has emerged as the m ost versatile architecture for parallel com putations. However, the num ber of nodes m in a hypercube is a power of 2, 2d, where d is
more » ... e dimension of the hypercube. In practice, it m ay not be possible to have a complete hypercube be cause the cost of upgradation is proportional to the num ber of nodes. Incomplete and Composite hypercubes help remove th e exponential node(and hence cost) constraint. In this thesis we establish the equality of m-node composite and incom plete hypercubes. Then we identify a class of algorithm s designated Fully Normal Algorithms for im plem enting a variety of algorithm s on composite hypercubes. We define critical size of a com posite hypercube to help identify th e performance bounds and com pute the speedup achieved. Finally, we develop a set of graph algorithm s th a t can be used as building blocks. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UM I a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.
doi:10.1109/ipps.1991.153770 dblp:conf/ipps/PrabhalaS91 fatcat:tzikjfnxx5gvdexvcc4m55gnqe