Combinatorial and Computational Properties of a Diameter Constrained Network Reliability Model

This paper is intended as a summary of combinatorial and computational properties of a Diameterconstrained network reliability model. Classical network reliability models are based on the existence of end-toend paths between network nodes, not taking into account the length of these paths; for many applications this is inadequate because the connection will only be established or attain the required quality if the distance between the connecting nodes does not exceed a given value. An alternative topological reliability model is the Diameter-constrained reliability of a network (DCR); this measure considers not only the underlying topology, but also imposes a bound on the diameter, which is the maximum distance between the nodes of the network. As communication networks can be modeled by undirected as well as directed graphs, we present a synopsis of the results known up until now pertaining the DCR for both topological representations. Moreover we show some important combinatorial properties of this model, and as a consequence we also prove well-known properties of the classical network reliability measure (i.e., where no distance constraints are imposed on the paths connecting the nodes of a network) as the DCR subsumes the classical network reliability measure. Key–Words: Reliability, networks, diameter, computational complexity.