Reliable broadcasting in product networks with Byzantine faults

The reliability of broadcasting in product networks is discussed. We assume that a network may contain faulty nodes and/or links of Byzantine type and that no nodes know any information about faults in advance. If there are n independent spanning trees rooted at the some node of a network, the network is called an n-channel graph. We first show a construction of n independent spanning trees rooted at the same node of a product network consisting of n component graphs. Then we design a broadcasting scheme in the product network so that messages are sent along the n independent spanning trees. This broadcasting scheme can tolerate up to [(n-1)/2] faults of Byzantine type even in the worst case. Broadcasting by the scheme is successful with a probability higher than 1-k^-[n/2] in any product network of order N consisting of n component graphs of order b or less if at most N/4b³nk faulty nodes are randomly distributed in the network. Furthermore we show how to construct n₁+n₂ independent spanning trees in a product network of two graphs such that the one component graph is an n₁-channel graph and the other component graph is an n₂-channel graph. These independent spanning trees can be also used as efficient and reliable message channels for broadcasting in the product network