Fault-Tolerant Embedding Algorithm for Complete Binary Tree in Hypercube

초록

In this paper, we will propose a scheme which maps complete binary tree to a faulty hypercube. Recent researcheres showed that if no more than n-1-[log2n] nodes/links are removed from n-cube, there still exists an (n-1)-lovel complete binary tree with dilation 1. It was also proved that with given n-2 faults, an n-level complete binary tree with dilation 2 can be embedded in an n-cube such that all tree nodes are fault-free except at the nth level. 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 topdown algorithm has low time complexity, i.e., o(n2). It also guarantees run-time fault tolerance by reconfiguring the embedded tree locally.