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<p><b>Abstract</b>—The mesh-connected multiprocessor has become popular for its simple and regular structure. In this paper, a new data structure, the <tmath> R{\hbox{-}}{\rm{array}} </tmath>, is proposed to represent the mesh at first. The element in the <tmath> R{\hbox{-}}{\rm{array}} </tmath> stores the statistical information about the occupied conditions of the mesh. The statistical information of the <tmath> R{\hbox{-}}{\rm{array}} </tmath> can direct the allocation process to jump to the processors that can serve as a base of a free submesh. Based on a simple and reasonable assumption, we develop a stochastic process to analyze the behaviors of the proposed scheme. The proposed scheme is the first one whose probabilities of locating free submeshes under different workloads are precisely computed. These results can be applied to each full-recognition scheme. In addition, the execution costs of the proposed scheme can also be accurately calculated. Finally, the simulations are performed. Compared with a lot of the previous schemes, the simulations show that the proposed schemes are faster than most of them.</p>
Allocation, mesh, first-fit, best-fit, buddy, Markov chain, random walk.

C. Hsu, L. Chou and F. Wu, "Processor Allocation in the Mesh Multiprocessors Using the Leapfrog Method," in IEEE Transactions on Parallel & Distributed Systems, vol. 14, no. , pp. 276-289, 2003.
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