Embedding of Fault-Tolerant Trees in the Josephus Cube

P Loh
2002 Parallel Processing Letters  
The tree interconnection network lends itself to several suitably structured applications. However, the low connectivity at each node, traffic congestion and single point of failure at the root node reduce reliability and availability. Both the hypertree and X-tree are faulttolerant variants of the basic tree network and have been the focus of more recent implementation and research interest. In this paper, we introduce a recently proposed family of interconnection networks known as the
more » ... Cubes and show how hypertrees, X-trees and ringed X-trees of arbitrary height can be near-optimally embedded in this novel interconnection network. Embedding techniques used for both hypertree and Xtrees are simple and may be recursively applied. The average inter-node distance in such a tree network, however, increases as lgN, where N is the network size. While the tree has smaller diameter than the mesh, it does not exploit physical locality as effectively [1, 11]. In particular, many algorithms can make use of direct communication between the leaf nodes if it exists. For applications that require extensive communication between leaf nodes, this property may prove to be a serious disadvantage. Additionally, the single root node in the case of the single-rooted binary tree could present severe traffic congestion and a single point of failure. Even in the case of the double-rooted tree, failure or severe congestion at any root node disconnects both left and right halves of the network. Fault-tolerant tree interconnection structures have been proposed to overcome these disadvantages. These include the hypertree and X-tree, which are illustrated in Figure
doi:10.1016/s0129-6264(02)00077-x fatcat:4z5wv567ubaeliog2t5b2zsosy