By Selim G. Akl
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4. N o t e t h a t each of the two (n/2) x (n/2) merging networks is constructed by applying t h e s a m e rule recursively, t h a t is, by using t w o (n/4) x (n/4) merging net works followed by a r a n k of (n/2) - 1 c o m p a r a t o r s . T h e correctness of this m e t h o d , k n o w n as O d d - E v e n Merging, is established in the following theorem. }, respectively, (2) then computing c2i = min(di +l, ei) and c2i + l = m a x ( r f / + ,1 ei) for i = 1, 2 , n - l (3) and finally letting cx = dx a n d c2n = en.
M . , a n d T h o m p s o n , C. D . (1982). R E S S T : A V L S I i m p l e m e n t a t i o n of a r e c o r d - s o r t i n g stack, Tech. R e p . N o . U C B / C S D 82/102, C o m p u t e r Science Divi sion, U n i v e r s i t y of California, Berkeley, California, April 1982. 38 2 NETWORKS FOR SORTING C h e n , T. C , E s w a r a n , K . , L u m , V. Y , a n d Tung, C. (1978a). Simplified o d d - e v e n sort using m u l t i p l e shift-register loops, Internat. J. Comput. Information Sci.
A n d K u n g , H . T. (1977). S o r t i n g o n a m e s h - c o n n e c t e d parallel c o m p u t e r , Comm. ACM 20 (4), 2 6 3 - 2 7 1 . Todd, S. (1978). A l g o r i t h m s a n d h a r d w a r e for a m e r g e sort using m u l t i p l e processors, IBM J. Res. Develop. 22 (5), 5 0 9 - 5 1 7 . Yasuura, H . , Tagaki, N . , a n d Yajima, S. (1982). T h e parallel e n u m e r a t i o n s o r t i n g s c h e m e for V L S I , IEEE Trans. Comput. C-31 (12), 1192-1201.