On the Fault-tolerant Embeddings of Complete Binary Trees in Mesh Interconnection Networks

In this article, several schemes are proposed for embedding complete binary trees (CBT) into meshes. All of the proposed methods outperform those in the previous studies. First, a link congestion 1 embedding is achieved. Its expansion ratio is at the lowest level as we know now. Except for this superiority, it also provides another capability for fault tolerance to resist abnormal system faults, thus the embedding structure can be more guaranteed and the node utilization is raised further. Second, a link congestion 1 embedding with no-bending constraint is obtained. This scheme provides efficient CBT embedding for both the optical mesh and general mesh at the same time while keeping those good properties as the previous scheme. The last one is an optimal embedding which is applied to a 3D cubic mesh, where the node is almost fully utilized and its link congestion is 2. 2002 Elsevier Science Inc. All rights reserved.