Multiple regular graph embeddings into a hypercube with unbounded expansion

As topological structures, interconnection networks play an important role in parallel and distributed computer systems, particularly in multicomputer systems, which provide an effective mechanism for exchanging data between processors. In this paper, we study the node-fault-tolerant capability of an n-dimensional hypercube with respect to multiple regular graph embeddings into a hypercube with unbounded expansion. We present a fault-tolerant method for multiple regular graph embeddings into a hypercube with dilation 3, congestion 1, and load 1. These results show that O (n2 − ⌊log2l⌋2) faults can be tolerated where n is the number of dimensions in a hypercube and l is the number of the nodes of the regular graph. The presented embedding methods are mainly optimized for balancing the processor loads, while minimizing load and congestion as far as possible. Furthermore, our method expands on some previously known findings. Also, this technology can be applied in grid computing and cloud computing.