Efficient resource placement in hypercubes using multiple-adjacency codes

While a certain resource in the hypercube may be shared by cube nodes to lower the cost, multiple copies of a shared resource often exist in the hypercube to reduce contention, and thus the potential delay, in fetching any shared copy. It is desirable that one employs as few resource copies as possible to ensure that every node is able to reach the resource in a given number of hops, achieving efficient resource placement. This placement method also keeps system performance degradation minimal after one resource copy becomes unavailable due to a fault. First, we consider placing multiple copies of a certain resource in a way that every cube node without the resource is adjacent to a specified number of resource copies. The use of our developed perfect and quasiperfect multiple-adjacency codes makes it possible to arrive at efficient solutions to this placement problem in a simple and systematic manner for an arbitrary hypercube. We then deal with the generalized resource placement in the hypercube such that every node without the resource can reach no less than a specified number of resource copies in no more than a certain number of hops, using as few resource copies as possible. Our placement results yield lowest potential access contention for a given number of resource copies (i.e., cost), particularly useful for large-scale hypercubes.<
>