Distributed Fault-Tolerant Embeddings of Rings in Incrementally Extensible Hypercubes with Unbounded Expansion

Abstract

The Incrementally Extensible Hypercube (IEH) is a generalization of interconnection network that is derived from the hypercube. Unlike the hypercube, the IEH can be constructed for any number of nodes. That is, the IEH is incrementally expandable. In this paper, the problem of embedding and reconfiguring ring structures is considered in an IEH with faulty nodes. There are a novel embedding algorithm proposed in this paper. The embedding algorithm enables us to obtain the good embedding of a ring into a faulty IEH with unbounded expansion, and such the result can be tolerated up to O(n*log2m ) faults with congestion 1, load 1, and dilation 4. The presented embedding methods are optimized mainly for balancing the processor loads, while minimizing dilation and congestion as far as possible.