Path Failure in Cylinderical Mesh Networks

The problem of node failures in interconnection networks has been extensively studied. In this paper we deene the notion of a more catastrophic form of failure | path failure | in which a sequence of nodes from a source to a sink in the network fail. The corresponding collapse in the structural properties of the underlying network is analyzed in quantitative terms, as a function of network size, by using the notion of catastrophic failure. We examine this problem in a xed setting, that of the cylinderical mesh, a network designed to maximize the number of communication routes between a set of producers and a set of consumers. Our proofs use interesting graph theoretic and combinatorial techniques, and formally establish that connectivity is drastically eeected by path failure.