Multigrid Algorithms on the Hypercube Multiprocessor
IEEE Transactions on Computers
On the permutation capability of multistage interconnection networks
IEEE Transactions on Computers
Pyramidal systems for computer vision
A New Benes Network Control Algorithm
IEEE Transactions on Computers
Properties of multistage interconnection networks
Properties of multistage interconnection networks
Sorting in c log n parallel steps
Combinatorica
Journal of the ACM (JACM)
ISCA '85 Proceedings of the 12th annual international symposium on Computer architecture
Study of multistage SIMD interconnection networks
ISCA '78 Proceedings of the 5th annual symposium on Computer architecture
On Evil Twin Networks and the Value of Limited Randomized Routing
IEEE Transactions on Parallel and Distributed Systems
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The routing control of Benes networks has proven to be costly. This paper introduces a new approach to fast control of N × N 3-stage Benes networks of r × r crossbar switches as building blocks, where N = r2 and r ≥ 2. The new approach consists of setting the leftmost column of switches to an appropriately chosen configuration so that the network becomes self-routed while still able to realize a given family of permutations. This approach requires that, for any given family of permutations, a configuration for the leftmost column be found. Such a family is called compatible and the configuration of the leftmost column is called the compatibility factor. In this paper, compatibility is characterized and a technique to determine compatibility and the compatibility factor is developed. The technique is used to show the compatibility and find the compatibility factor of &OHgr;-realizable permutations, the permutations needed to emulate a hypercube, and the families of permutations required by FFT, bitonic sorting, tree computations, multidimensional mesh and torus computations, and multigrid computations. An O(log2 N) time routing algorithm for the 3-stage Benes will also be developed. Finally, as only 3 compatibility factors are required by the above families of permutations, it will be proposed to replace the first column by 3 multiplexed connections yielding a self-routing network with strong communication capabilities.