8,651 research outputs found
Expanded delta networks for very large parallel computers
In this paper we analyze a generalization of the traditional delta network, introduced by Patel [21], and dubbed Expanded Delta Network (EDN). These networks provide in general multiple paths that can be exploited to reduce contention in the network resulting in increased performance. The crossbar and traditional delta networks are limiting cases of this class of networks. However, the delta network does not provide the multiple paths that the more general expanded delta networks provide, and crossbars are to costly to use for large networks. The EDNs are analyzed with respect to their routing capabilities in the MIMD and SIMD models of computation.The concepts of capacity and clustering are also addressed. In massively parallel SIMD computers, it is the trend to put a larger number processors on a chip, but due to I/O constraints only a subset of the total number of processors may have access to the network. This is introduced as a Restricted Access Expanded Delta Network of which the MasPar MP-1 router network is an example
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The effect of FPU architecture on a dynamic precision algorithm for the solution of differential equations
Solution of lnitial Value Problems (IVPs) is an important application in scientific computing. Methods for solving these problems use techniques for reducing the error and increasing the speed of the computation. This paper introduces a class of algorithms which dynamically reconfigure their operating parameters to reduce the computation time. By dynamically varying the precision of the arithmetic being performed, it is possible to obtain dramatic speedups on certain architectures when solving IVPs. This paper illustrates how various architectures impact on a dynamic precision version of the Runge-Kutta-Fehlberg algorithm. It is shown that a speedup of over 30 percent is possible for both massively parallel processors and vector supercomputers
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Self-routing lowest common ancestor networks
Multistage interconnection networks (MIN's) allow communication between terminals on opposing sides of a network. Lowest Common Ancestor Networks (LCAN's) [1] have switches capable of connecting bi-directional links in a permutation pattern that additionally permits communication between terminals on the same side. Self-routing LCAN's have interesting permutation routing capabilities and are highly partionable. This paper characterizes self-routing LCAN's and analyzes their permutation routing capabilities. It is shown that the routing network of the CM-5 is a particular instance of an LCAN
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Lowest common ancestor interconnection networks
Lowest Common Ancestor (LCA) networks are built using switches capable of connecting u + d inputs/outputs in a permutation pattern. For n source nodes and I stages of switches, n/d switches are used in stage l - n/d - u/d in stage l - 2, and in general , n-u^l-i-l/d^l-i switches in stage i. The resulting hierarchical structure possesses interesting connectivity and permutational properties. A full characterization of LCA networks is presented together with a permutation routing algorithm for a family of LCA networks. The algorithm uses the network itself to collect and disseminate information about the permutation. A schedule of O(dp log_d/u n) passes is obtained with a switch set-up cost factor of O(log_d/u n) (p is the minimum number of passes that an algorithm with global knowledge schedules)
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Shortest paths in orthogonal graphs
Orthogonal graphs were introduced as a simple but powerful tool for the description and analysis of a class of interconnection networks. Routing, and hence finding shortest paths between any two nodes of an orthogonal graph, becomes an important problem. It is shown in this paper that routing in this class of graphs reduces to a node covering problem in the bipartite coverage graph of the orthogonal graph. A minimum cover clearly leads to a shortest path. In general, the problem of finding the mÃnimum node cover in a bipartite graph is NP-complete. However, the bipartite coverage graphs corresponding to orthogonal graphs have a regular pattern of edges. This allows the development of a routing algorithm which results in a minimum cover. The procedure executes in polynomial time in the number of bit-nodes of the bipartite graph. It therefore results in a shortest path algorithm whose time complexity is quadratic in the logarithm of the number of nodes in the original orthogonal graph
On exact mappings between fermionic Ising spin glass and classical spin glass models
We present in this paper exact analytical expressions for the thermodynamical
properties and Green functions of a certain family of fermionic Ising
spin-glass models with Hubbard interaction, by noticing that their Hamiltonian
is a function of the number operator only. The thermodynamical properties are
mapped to the classical Ghatak-Sherrington spin-glass model while the the
Density of States (DoS) is related to its joint spin-field distribution. We
discuss the presence of the pseudogap in the DoS with the help of this mapping.Comment: 6 page
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
The characteristic identity formalism discussed in our recent articles is
further utilized to derive matrix elements of type 2 unitary irreducible
modules. In particular, we give matrix element formulae for all
gl(m|n) generators, including the non-elementary generators, together with
their phases on finite dimensional type 2 unitary irreducible representations.
Remarkably, we find that the type 2 unitary matrix element equations coincide
with the type 1 unitary matrix element equations for non-vanishing matrix
elements up to a phase.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.424
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