Resource Allocation in Hypercube Systems

Optimal allocation of multiple copies of resources is studied in this paper. our objective is to allocate these resource to nodes of the hypercube in such a way that every node can reach some copy with small number of hops. An allocation is evaluated by defining a performance measure, resource diameter, which is the m&mum number of hops any node has to take to reach a copy of resource. We have developed computationally efficient algorithms to obtain optimal or near-optimal allocations in n-dimensional hypercubes. Two strategies are presented to allocate a given number of (a power of 2) copies of a resource in a hypercube. In the basic strategy equal number of copies are allocated to subcubes. By applying this strategy recursively, we can obtain an allocation in n-dimensional cube with 2k copies that will have a resource diameter of 1-1. We can obtain better performance with the hierarchical strategy which is based on perfect codes [5, 71 and the basic strategy. The second approach is algorithmic and an optimal partitioning of cubes for allocation can be selected efficiently. Some special cases whose allocations are not obvious are also discussed. In addition, the problem of finding the minimum number of resource copies required to achieve a specified resource diameter in a hypercube is solved.