. A. Gottlieb, C. P. Kruskal. Complexity results for permuting data and other computations on parallel processors, J. ACM, Vol. 31, No. 2, 193-209(April 1984).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Theorem 5.2 applies with an improved multiplicative constant of 1 Gammao(1) 2 . 6 Concluding Remarks The upper and lower bounds for network selection discussed in this paper significantly improve on previously known results when the number of keys at each processor, n=p, is sufficiently large [10]. In proving lower bounds, it was assumed that n and p are powers of 2, and that every processor begins with exactly n=p keys. The proofs can easily be extended to handle arbitrary values of n and p (losing at most a constant factor) and arbitrary initial distributions of the keys. Theorem 5.1 ....

A. Gottlieb and C. P. Kruskal. Complexity results for permuting data and other computations on parallel processors. JACM, 31:193--209, 1984.

.... or can be determined at compile time [6, 9] The permutation capability is an important measure that indicates how efficient a network is in supporting static or compiled communications, and a large body of research efforts has been devoted to the subject in the past in either packetswitched [10, 16, 21, 29] or circuit switched [8, 27, 30] non multiplexed networks. One of our main contributions is the determination of the minimummultiplexing degree needed in LM and in PM, respectively, for a network to be rearrangeably nonblocking, that is, to be able to embed any permutation off line. We obtain ....

A. Gottlieb and C.P. Kruskal. Complexity results for permuting data and other computations on parallel processors. Journal of ACM, 31(2):193-- 209, 1983.

.... related is the work reported in [6, 7, 8] where asymptotic lower bounds on the number of wavelengths required to make a general WDM network nonblocking in PM were obtained (LM was not considered) In addition, the subject of permutation scheduling in non multiplexed networks has been treated in [9, 10, 11, 12] and elsewhere. Finally, comparisons of LM and PM in terms of the blocking probability of dynamically generated requests for connection in WDM networks have been made [5, 13, 14, 15] So have the comparisons in terms of the communication latency as well as blocking probability in TDM networks ....

A. Gottlieb and C. Kruskal, "Complexity results for permuting data and other computations on parallel processors," Journal of ACM, vol. 31, no. 2, pp. 193--209, 1983.

....(n 16) Problem 17 Is it possible to perform deterministic sorting on the MIMD n dimensional binary hypercube in O(n) steps We have concentrated here on the saturated case, where the number of data elements matches the number of processors. For sorting techniques when p N refer to [56, 90, 208, 318]. 4.7 Hypercubic and Related Networks We provide references to known results on the MIMD cube connected cycle, de Bruijn, shuffle exchange, hypermesh, and generalized hypercube. In general, communication on an N node bounded degree network can be simulated on any hypercubic network with only ....

Gottlieb, A., and Kruskal, C. P. Complexity results for permuting data and other computations on parallel processors. J. ACM. 31 (2), 1984, pp. 193--209.

....a measure of irregularity. 3.1 Local and global inefficiency. In the following, we extend the definitions in [45] to take into account the above comments. For a sequential algorithm A, we denote by t(x; n) its sequential running time on an input x of size jxj = n. For a parallel size independent [40] algorithm B that solves the same problem, we denote by t p (x; n) its running time on a p PRAM with 1 p h(n) Thus, t p is a function of x, n and p, p being a free parameter. As in [42] the parallel work w p (x; n) denotes the number of operations effectively performed by the algorithm B. We ....

A. Gottlieb and C.P. Kruskal. Complexity results for permuting data and other computations on parallel processors. J. ACM, 31:193--209, 1984.

....among a given set of processor nodes such that communications can be performed as quickly as possible. This research investigates ways of interconnecting large numbers of processors using smaller ATM switches. The major subjects addressed here are: network topology design, embedding and routing [1, 2, 7, 8, 11, 18, 22]. 1.1 Network Topology Design Several different criteria must be considered when designing an interconnection network. Graph theoretic metrics have been used to characterize network topologies but application specific requirements can also be important. Many networks used for MPP machines are ....

Allan Gottlieb and Clyde P. Kruskal. Complexity Results for Permuting Data and Other Computations on Parallel Processors. J. Assoc. for Computing Machinery, 31(2):193--209, Apr. 1984. Presents low bounds on certain parallel processors.

....Work There is a lot of literature dealing with more practical models of parallel computation. See the papers of Chin [4] and Heywood and Leopold [11] for recent surveys. We only mention some papers with close relations to our work. Perhaps the closest relationship is with Gottlieb and Kruskal [10]. They also study the phenomenon of a more efficient use of parallel machines through enlargement of problem sizes. For example, they introduce the so called supersaturation limit, which, informally speaking, asks how the relation of input size to number of processors has to be in order to get an ....

....algorithm that is optimal provided that log 2 p = O(log n) in their setting. It is thus in their class ANC (almost efficient NC fast) Translated into our setting that means that they get a completely parallelizable sorting algorithm under the same conditions as already Gottlieb and Kruskal [10] do. Note that although our BRAM used has unbounded degree, that is, global memory size p 2 , due to the small number of large, blocked communications these data exchanges can also be performed on bounded degree networks without time loss. In essence, this already follows from Kunde s ....

A. Gottlieb and C. P. Kruskal. Complexity results for permuting data and other computations on parallel processors. J. ACM, 31(2):193--209, April 1984.

....where such a precision is fully acceptable because it adds only the additive term f(n) to the failure probability. However, there are some critical application (e.g. in cryptography) where such a deviation from the uniform distribution might be dangerous. Due to results of Gottlieb and Kruskal [7], permutation generation cannot be too fast in models, where a processor may communicate only with a small and fixed number of other processors. Since we are interested in very fast permutation generation, we turn our attention to the PRAM model, for which such communication limitations do not ....

A. Gottlieb and C. P. Kruskal, Complexity results for permuting data and other computations on parallel processors, J. Assoc. Comput. Mach. 31 (1984) 193--209.

....be noted that systems that depend on exploiting data locality and nearest neighbor connections to get good performance are generally more difficult to program. The NYU Ultracomputer project began by investigating parallel algorithms on message passing, staticly connected shuffle exchange machines [56, 122] and evolved in the direction of implementing an approximation to the parallel random access (PRAM) model of computation first described in [47] because of the greater ease and generality of this model for the programmer and implementation of software systems. This evolution included the ....

Allan Gottlieb and Clyde P. Kruskal. Complexity results for permuting data and other computations on parallel processors. Journal of the ACM, 31(2):193--209, April1984.

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. A. Gottlieb, C. P. Kruskal. Complexity results for permuting data and other computations on parallel processors, J. ACM, Vol. 31, No. 2, 193-209(April 1984).

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A. Gottlieb, C. P. Kruskal, "Complexity results for permuting data and other computations on parallel processors," J. ACM, vol. 31, no. 2, pp. 193-209, Apr. 1984.

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A. Gottlieb, C. P. Kruskal, Complexity results for permuting data and other computations on parallel processors, J. of the ACM 31, pp. 193--209, 1984.

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