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By Harry A.G. Wijshoff

The association of information is obviously of significant value within the layout of excessive functionality algorithms and architectures. even supposing there are a number of landmark papers in this topic, no entire 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 will exhibit the intrinsic complexity of knowledge or­ ganization for particular architectures. We follow this version of computation to a number of present parallel desktop architectures, e.g., the CDC 205 and CRAY vector-computers, and the MPP binary array processor. The learn of information association in parallel computations used to be brought as early as 1970. throughout the improvement of the ILLIAC IV method there has been a necessity for a thought of attainable information preparations in interleaved mem­ ory structures. The ensuing idea dealt basically with garage schemes often known 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 follow the speculation of skewing schemes to var­ ious varieties of parallel machine architectures. This leads to a few results for either the layout of parallel desktop architectures and for purposes of parallel processing.

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40 CHAPTER 2. 5: Extending a partial tessellation to a total tessellation. 1. 6: The conflict-regions of some templates. The conflict-region of a template P is the set of points that are forced to be stored into a memory bank different from (0,0, ... , 0) E Zd in a valid skewing scheme for P. 6 some examples of templates on the plane are depicted together with their conflict-region. 5. 4 Let P be a template on a d-dimensional array. ,P(znH of instances of P such that (i) for all i, 1 ~ i ~ n, P(zd ~ Cp and 0 f/.

4 Other Parallel Computer Architectures A great variety of parallel computer architectures have been proposed and developed that do not rely on a grid network but on some other kind of interconnection structure for the processing elements. Conunon interconnection structures that can be distinguished are: • n-dimensional grid networks • tree networks • pyramid networks CHAPTER 1. 8. Some examples of parallel computer architectures that use these interconnection networks are: the EGPA (Erlangen General Purpose Array [HHS76]) and the HAP (Hierarchical Array Processor system [Shi86]) both using a pyramid network, the COSMIC CUBE [Pea77] based on the n-dimensional cube network, and the shufRe-exchange computer as studied by Stone [Sto71] and the FFT networks [Ber72] both using the perfect shufRe network.

If T is of type 1 then (i) is fulfilled, and if T is of type 2 then (ii) is fulfilled. 5 Let Bl be a (Pl, 1) X (P2, 1)-block template and B2 a (ql, 1) X (q2, I)-block template, Pl < ql and PlP2 = qlq2 = N. Then the ezistence of a skewing scheme s : Z2 that Pllql. -t {O, 1, ... , N -I} that is valid for Bl and B2 implies Proof Let s be a skewing scheme that is valid for Bl and B 2 • Suppose Pl f ql· Consider any slice of the plane of width ql and height N. 12). Consequently there are exactly q2 points within this slice with a s-value of m, for every m E {O, 1, ...

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