Data Organization in Parallel Computers by Harry A.G. Wijshoff

By Harry A.G. Wijshoff

The association of knowledge is obviously of serious significance within the layout of excessive functionality algorithms and architectures. even supposing there are numerous landmark papers in this topic, no accomplished remedy has seemed. This monograph is meant to fill that hole. We introduce a version of computation for parallel computing device architec­ tures, during which we can exhibit the intrinsic complexity of knowledge or­ ganization for particular architectures. We follow this version of computation to a number of present parallel computing device architectures, e.g., the CDC 205 and CRAY vector-computers, and the MPP binary array processor. The research of knowledge association in parallel computations used to be brought as early as 1970. in the course of the improvement of the ILLIAC IV procedure there has been a necessity for a idea of attainable info preparations in interleaved mem­ ory structures. The ensuing conception dealt essentially with garage schemes also referred to as skewing schemes for 2-dimensional matrices, i.e., mappings from a- dimensional array to a couple of reminiscence banks. through the version of computation we can observe the idea of skewing schemes to var­ ious varieties of parallel desktop architectures. This leads to a few effects for either the layout of parallel laptop architectures and for purposes of parallel processing.

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Proof ~ Let s be a valid skewing scheme for {Ph P2 , ••• , Pt }. Consider the arrangement A in which an instance of Pi is located at every point P with s(p)=O. ) Any two instances Pl and Pl in A must be disjoint. ) To prove that A is a tessellation we need ~o show that every point q is covered. Consider the N possible instances of ~ that cover q and let their handles be located in points Pi (1 ~ j ~ N). 1) and thus there is exactly one Pic such that covers and II(PIc)=O. This is indeed in A by definition.

A second result of Shapiro [Sha78b] determines the validity of skewing schemes for a collection of templates of equal size. Shapiro showed that there is a valid skewing scheme for a template P if and only if P tessellates the d-dimensional space. As the argument is important, we briefly digress and include our simplified proof of this fact (cf. 2 below). 1. 1 Let P l and P2 be instances of P with handles located in hl E Z4 and h2 E Z4 respectively. Pl and P2 overlap if and only if hl and h2 can be covered by a single instance of P.

The algorithm of composition will be explained below. 13 the "suitable" Latin square can be any double diagonal Latin square when q = 1 or q ~ 4, because the class of double diagonal Latin squares is obviously closed under direct (Kronecker-) product and double diagonal Latin squares exist for every such order (cf. 12). 683) notes that for n == ±1 (mod 6) a double diagonal Latin square is obtained by taking a( i, j) == j +2i - 2 (mod n). 12. 16: Diagonals in non-permuted order. 2 Composition of Double Diagonal (dd) Latin Squares Let a be a dd-Latin square of order p over the (barred) symbol set 1, ...

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