ASSTRACT. Let U1 , U2, . . . , Ud be totally ordered sets and let V be a set of n d-dimensional vectors In U~ X Us. . X Ud . A partial ordering is defined on V in a natural way The problem of finding all maximal elements of V with respect to the partial ordering ~s considered The computational complexity of the problem is defined to be the number of required comparisons of two components and is denoted by Cd(n). It is tnwal that C~(n) = n -1 and C,~(n) < O(n 2) for d _~ 2 In this paper we show: (1) C2(n) = O(n logan) for d = 2, 3 and Cd(n) ~ O(n(log2n) ~-~) for d ~ 4, (2) C,t(n) >_ flog2 n!l for d _> 2 KEY WORDS AND PHRASES: maxima of a set of vectors, computattonal complexity, number of comparisons, algorithm, recurrence CR CATEaOmES. 5.25, 5,31, 5.39

Methods for optimal assignments are given for instantaneous and sequential diagnosis procedures.

Approved f o r p u b lic r e le a s e ; d i s t r i b u t i o n u n lim ited DISTRIBUTION STATEMENT (of the abstract entered in B lo c k 20, If different from Report) SUPPLEMENTARY NOTES KEY WORDS (C ontinue on reverse side if necessary and ide n tify by block number)P a r a lle l p r o c e s s in g , VLSI d e s ig n , s o r t in g , F ou rier Transform ABSTRACT (Continue on reverse side If necessary and id e n tify by block number)We in trod u ce an in te r c o n n e c tio n p a tte rn o f p r o c e s s in g elem en ts, the cu bec o n n e c t e d -c y c le s (CCC), which can be used as a gen era l purpose p a r a l l e l p r o c e s s o r . Because i t s d esig n com p lies w ith p resen t t e c h n o lo g ic a l c o n s t r a in t s , the CCC can a ls o be used in the layou t o f many s p e c ia liz e d la rg e s c a le i n t e grated c i r c u i t s (VLSI). By com bining the p r in c ip le s o f p a r a lle lis m and p ip e lin in g , the CCC can emulate the cu b e-con n ected machine and the p e r fe c t s h u ffle w ith no s i g n i f i c a n t d egra d a tion o f perform ance but w ith a more compact s t r u c t u r e . We d e s c r ib e in d e t a i l how t o program the CCC fo r e f f i c i e n t l y Keywords : P a r a lle l p r o c e s s in g , VLSI d e sig n , s o r t in g , F o u rie r Transform .

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