On finding optimum paths in computer networks

We consider the problem of finding an optimum path from each node in the network to a destination node in the network. Typically, each edge in the network is assigned a weight value (e.g. bandwidth or delay), and a metric function (e.g. min or +) is applied consecutively to the edges in the path. The result is the metric value of the path. However, some metric functions have conflicts, and prevent all nodes from obtaining an optimum path simultaneously. Conditions to ensure that a metric function is conflict-free have been presented in the literature. In this study, we consider the more general problem where the optimality of the path is not a function of the edge weights but a function of the path itself. We therefore define a path ranking function, and give sufficient conditions for the ranking to be conflict free. Furthermore, a distributed algorithm is presented to obtain the optimum path from each node to the destination