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Finite field for scientists and engineers
Deadlock-Free Message Routing in Multiprocessor Interconnection Networks
IEEE Transactions on Computers
Topological Properties of Hypercubes
IEEE Transactions on Computers
Performance of the Direct Binary n-Cube Network for Multiprocessors
IEEE Transactions on Computers
Performance Analysis of k-ary n-cube Interconnection Networks
IEEE Transactions on Computers
Introduction to algorithms
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Minimum deadlock-free message routing restrictions in binary hypercubes
Journal of Parallel and Distributed Computing
The turn model for adaptive routing
Journal of the ACM (JACM)
A Cost and Speed Model for k-ary n-Cube Wormhole Routers
IEEE Transactions on Parallel and Distributed Systems
An optimal routing algorithm for mesh-connected Parallel computers
Journal of the ACM (JACM)
Digital Image Processing
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In this paper, we address the problem of minimizing channel contention of linear-complement communication on wormhole-routed hypercubes. Our research reveals that, for traditional routing algorithms, the degree of channel contention of a linear-complement communication can be quite large. To solve this problem, we propose an alternative approach, which applies processor reordering mapping at compile time. In this compiler approach, processors are logically reordered according to the given communication(s) so that the new communication(s) can be efficiently realized on the hypercube network. It is proved that, for any linear-complement communication, there exists a reordering mapping such that the new communication has minimum channel contention. An $O(n^3)$ algorithm is proposed to find such a mapping for an $n \hbox {-} {\rm dimensional}$ hypercube. An algorithm based on dynamic programming is also proposed to find an optimal reordering mapping for a set of linear-complement communications. Several computer simulations have been conducted and the results clearly show the advantage of the proposed approach.