Bounding the Size of k-Tuple Covers

Suppose there are n applications and n processors. A pair cover is a set S of one-to-one mappings (assignments) of the applications to the processors such that, for every pair (Ai,Aj) of applications and every pair (p,q) of processors, there is an assignment f in S that maps (Ai,Aj) to (p,q). More generally, we consider, for all k/spl ges/1, minimum size k-tuple covers. We improve bounds given earlier in by Latifi, where the application for k-tuple covers was fault tolerance of the multidimensional star network. Let F(n,k) denote the minimum cardinality k-tuple cover for n applications and processors. We give bounds for F(n,k) that are within a small multiplicative factor of optimum.