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<p><it>Abstract—</it>This paper addresses task allocation schemes for MIN-based multiprocessors. Two types of allocation policies, <b><it>cubic</it></b> and <b><it>noncubic</it></b>, are discussed here. Conflicts through the network and inability to partition the system effectively are the main bottlenecks in a MIN-based system. To solve both the problems, a renaming scheme for input and output ports of a MIN is proposed. We use the baseline MIN as an example in this work and call the renaming scheme as <b><it>bit reversal</it></b> (<b><it>BR</it></b>) <b><it>matching</it></b><b><it>pattern</it></b>. Allocation with the new matching pattern minimizes conflicts and partitions the system completely into independent subsystems. The novelty of this matching pattern is that we can use any dynamic cubic allocation and/or scheduling scheme developed for the hypercubes also for the MIN machines. The BR matching pattern can be used with any kind of MIN. An allocation policy for noncubic tasks is also presented with this matching pattern. Various performance measures with different allocation algorithms are compared via simulation. The advantages of the algorithms with the proposed matching pattern are shown in terms of system efficiency, delay and task miss ratio.</p>

C. R. Das and C. Yu, "Disjoint Task Allocation Algorithms for MIN Machines with Minimal Conflicts," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 373-387, 1995.
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