A Comparative Study Of X-Tree, Pyramid And Related Machines

The intent of this paper was to investigate data movement techniques for some special networks which are derived from the binary tree and the mesh machines. We presented optimal bounds for some problems and close bounds for others. A new lower bound technique which incorporates the entire network topdogy was introduced. We believe that this technique is quite powerful and can be exploited to yield good lower bounds for conservative flow algorithms on other networks. However, it seems to be diacult to generalize it for nonconservative flow algorithms. Though we have obtained close bounds, several problems that remain open are noted.