Embedding a complete binary tree into a faulty supercube

The supercube is a novel interconnection network that is derived from the hypercube. Unlike the hypercube, the supercube can be constructed for any number of nodes. That is, the supercube is incrementally expandable. In addition, the supercube retains the connectivity and diameter properties of the corresponding hypercube. In this paper, we consider the problem of embedding and reconfiguring binary tree structures in a faulty supercube. Further more, for finding the replaceable node of the faulty node, we allow 2-expansion such that we can show that up to (n-2) faults can be tolerated with congestion 1 and dilation 4 that is (n-1) is the dimension of a supercube.