Embedding of complete binary tree with 2-expansion in a faulty Flexible Hypercube

Although the embedding of complete binary trees in faulty hypercubes has received considerable attention, to our knowledge, no paper has demonstrated how to embed a complete binary tree in a faulty Flexible Hypercube. Therefore, this investigation presents an algorithm to facilitate the embedding job when the Flexible Hypercube contains faulty nodes. Of particular concern are the network structures of the Flexible Hypercube that balance the load before as well as after faults start to degrade the performance of the Flexible Hypercube. Furthermore, to obtain the replaceable node of the faulty node, 2-expansion is permitted such that up to (n-2) faults can be tolerated with congestion 1, dilation 4 and load 1.