Embedding Large Complete Binary Trees in Hypercubes with Load Balancing

If G is not larger than H, and if the embedding is isomorphic, then there is no slowdown and the algorithm running on the system cannot tell the difference between G and H from the viewpoint of the above cost measures. When the guest graph is larger than the host graph, then the load of embedding must be at least VG/VH , where VG and VH are the numbers of nodes in the guest and host, respectively. If the load is VG/VH , then the load of embedding is balanced. In this case, the slowdown of emulation is S 5 O(VG/VH) if dilation and congestion are O(1). When we pay special attention to the common requirements of algorithms developed for the guest architecture, it may be possible to remove the big-oh notation from the slowdown expressions, and define strict requirements for optimality of emulations. This is possible because most parallel architectures have their corresponding favorite computation types for which they are topologically well suited. JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 35, 104–109 (1996) ARTICLE NO. 0073