Placement of resources in the star network

In a large system with many processing elements (PE), it is very expensive to equip each PE with a copy of the resource. It is desirable to distribute few copies of a given resource to ensure that every PE is able to reach a copy of that resource within a certain number of hops. Previous work has been done on the binary hypercube as well as on the k-ary n-cube. We consider the problem of resource sharing among PEs in the star interconnection network (SIN) and present three different placement strategies. First, we consider the perfect 1-adjacency resource placement. In this placement, resources have to be distributed in such a way that every node without a copy of the resource will find exactly one node adjacent to it having a copy of the resource. Second, the perfect full adjacency placement is considered. In this placement each node without a copy of the resource will find all nodes adjacent to it having a copy of the resource. Finally, the perfect 2-adjacency placement is considered where each non resource node is adjacent to exactly two resource copies. We show that a perfect 2-adjacency resource placement does not exist for all star networks