A link-disjoint subcube for processor allocation in hypercube computers

Abstract

We propose a new type of subcubes, called link-disjoint subcubes (LS), which can be used for the subcube allocation problem in hypercube computers. A link-disjoint subcube is not a contiguous subcube as in the previous schemes, but this subcube still has no common communication link with any other subcubes. When link-disjoint subcubes are used, the performance degradation caused by non-contiguous processor allocation is lower than 1.0% in many cases. With the availability of link-disjoint subcubes, there are [n/2](n-2)C(k-1)2(n-k) k-dimensional LSs recognizable in an n-dimensional hypercube. The number of all the recognizable subcubes under our allocation scheme is ([n/2](n - k)k + n(n - 1))/n(n - 1) times that under the previous schemes. For example, the number of all the recognizable subcubes is at maximum 2.39 times that of contiguous subcubes in 10-dimensional hypercube computers, Through simulation, the performance of our scheme is measured and compared to the previous schemes in terms of processor utilization and waiting delay. It has been shown through simulation that the LSs increase the performance of our allocation scheme.