Linear complexity algorithms for maximum advance deflection routing in some networks

We consider routing in a network with no buffers at intermediate nodes: packets must move in a synchronized manner in every time step until they reach their destinations. If contention prevents a packet from advancing, i.e. taking an outgoing link on a shortest path from its current node to its destination, it is deflected on a different link, hence the name deflection routing. One common strategy in the design of deflection routing algorithms is maximum advance, which advances a maximum number of packets at every node in every time step. We examine two settings: non capacitated networks and capacitated networks. We present linear complexity algorithms for maximum advance deflection routing in networks with topological properties as follows: When the network is non capacitated, we require that each packet can advance on at most two links from any intermediate node in the network. When the network is capacitated, we require a special condition on the links in addition to the one mentioned above. Metropolitan and wide area networks typically satisfy those conditions