This paper investigates the problem of a divisible nonlinear load distribution on homogeneous complete b-ary tree networks. Classic models of nonlinear computational loads omit several steps in processing the load and yield only an approximate distribution for fractional loads. This paper considers a new model of nonlinear computational loads that includes all load processing steps and yields a practical solution to distribute fractional loads. Two algorithms to distribute a divisible nonlinear load on homogeneous complete b-ary tree networks are proposed. Closed-form expressions for the parallel processing time and speed-up for complete b-ary trees are also derived. This paper demonstrates that the asymptotic speed-up of the proposed algorithms is the number of processors in a multicomputer system. The proposed algorithms improved the classic algorithm in terms of speed-up.

中文翻译：

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异构单级树上的可分非线性载荷分布

本文研究了齐次完全二叉树网络上的可分非线性负载分布问题。非线性计算载荷的经典模型在处理载荷时省略了几个步骤，并且仅产生部分载荷的近似分布。本文考虑了一种新的非线性计算载荷模型，该模型包括所有载荷处理步骤，并提供了一种用于分配部分载荷的实用解决方案。提出了在同构完全二叉树网络上分配可分非线性负载的两种算法。还导出了完整二叉树的并行处理时间和加速的封闭形式表达式。本文证明了所提出算法的渐近加速是多计算机系统中处理器的数量。