Embedding incomplete binary trees into incomplete hypercubes

It has been proved that an incomplete binary tree cannot be embedded into a n incomplete hypercube with dilation 1 and expansion 1. By applying some pr operties of inorder traversal, the authors present an embedding scheme with dilation 2 edge-congestion 2 and expansion ratio (N + 1)/N, where N is the number of nodes in an incomplete binary tree. The authors prove that this embedding is optimal under the constraint of expansion ratio (N + 1)/N. Wit h this embedding scheme, a method is developed that can be used to simulate a binary tree on an incomplete hypercube effectively. Under the distribute d environment, the mapping addresses of neighbouring nodes in an incomplete binary tree can be identified in constant time without repeating the mappi ng work. Furthermore, experimental results show that this scheme is much be tter than the corresponding best known dilation 1 embedding scheme in terms of hardware costs and implementation. Even in total time costs (addressing time, computation time and transmission time), this approach is quite comp etitive.