On the fault-tolerant embedding of complete binary trees in the pancake graph interconnection network

Abstract

This paper studies the problem of embedding complete binary trees ( CBTs) into an n-dimensional pancake graph ( P n ) with fault-tolerant capability. First, a new embedding scheme is developed for mapping a source CBT with height ∑ m=2 n⌊ log m⌋ and dilation 2 onto the P n . This scheme not only embeds a CBT whose height is very close to the largest possible one, but also saves a lot of unused generators and generator products. Furthermore, these unused generators and generator products are used to recover faulty nodes and embed multiple CBTs. Maximally, near 2/3 nodes of the source CBT are allowed to be faulty at the same time and can be recovered by our scheme with dilation 4. Alternatively, a scheme which can embed a CBT with height ∑ m=2 n⌊ log m⌋−1 is also given. In this case, if all nodes in the CBT are faulty, they can be recovered in the smallest number of recovery steps and only with dilation 4.