Efficient dynamic processor allocation for k-ary n-cube massively parallel processors

In this paper, we study the problem of allocating processors to application tasks for massively parallel processors (MPPs). Tasks are assumed to arrive dynamically and request processors interconnected in specific topologies. We extend the free-list strategy previously proposed for hypercube systems [2,3] to handle the processor allocation problem for MPPs with a k-ary n-cube interconnection, in which there is no wrap-around connection. The key to the extension is a novel way of representing sets of processors in the system by using [log2 k] × n ternary numbers. A problem which was not encountered in hypercube is that the same set of processors in k-ary n-cube could have different representations. As a result, tasks might not be allocated even if there are enough free processors, because the desired representation is not in the free list. We address this issue and give a solution to the problem. We also consider cases in which the number of processors requested by an incoming task is not a power of two (i.e., the noncubic allocation problem). Performance of the proposed schemes are evaluated in terms of their time complexity and effectiveness.