Optimal fault-tolerant communication algorithms on product networks using spanning trees

Over the last years cartesian product graphs have started to receive increasing attention as general class of networks for multiprocessor systems. One reason is that many efficient and popular networks such as the meshes, tori, hypercubes, hyper de Bruijn, product shuffle, and the newly proposed folded Petersen networks belong to this class of networks. Secondly, with the help of cartesian product graphs, a unique method for the design and analysis of a class of networks as well as techniques for embedding and communication algorithms can be provided. In this paper, first multiple arc-disjoint spanning trees are constructed on product networks with bidirectional links. These trees are utilized to design fault-tolerant algorithms for several important communication primitives assuming all-port communication. The problems under consideration include broadcasting, gossiping, scattering, and total exchange