Fault-Tolerant Embedding Algorithm for Complete Binary Tree in Hypercube

초록

Binary trees have been used frequently in parallel processing algorithms and their embedding on the hypercube is useful for various applications. In this paper, we will propose a sheme which maps complete binary tree to a faulty hypercube. Chan and et al. showed that(n-1)-level complete binary tree with dilation 1 can be embedded on an n-2 faulty n-cube but the embedding cannot be distributed onto each subcube. We will show that (n-1)-level complete binary tree with dilation 1 can be embedded in an n-dimensional hypercube with up to n-2 faulty nodes. The proposed top-down algorithm has low time complexity, i.e.,O(n²) using distributed parallel embedding. It also guarantees run-time faulty tolerance by reconfiguring the embedded tree locally