1. A method, comprising: transmitting a non-repeated reachability probe from a particular node into a shared-media network, the shared-media network connecting a plurality of nodes, wherein nodes that receive the non-repeated reachability probe are configured to reply to the particular node; determining a set of one or more nodes in the shared-media network that received the non-repeated reachability probe; determining, at the particular node, a minimum number of required nodes of the plurality of nodes that must act as routers in order to reach each of the plurality of nodes in the shared-media network; selecting, by the particular node, one or more routing nodes of the set of one or more nodes to act as the routers in the shared-media network based on the minimum number of required nodes; notifying, by the particular node, the selected one or more routing nodes of the one or more routing nodes of their selection; subsequently, dynamically adjusting, by the particular node, the minimum number of required nodes of the plurality of nodes that are selected as the one or more routing nodes of the set of one or more nodes based on network conditions; and wherein the steps of the transmitting the non-repeated reachability probe and the selecting the one or more routing nodes in response to a trigger selected from a group consisting of: a timer; determination that a number of unreachable nodes in the shared-media network has exceeded a first threshold; a determination that link quality in the shared-media network is below a second threshold; a detection of network perturbations; one or more new devices in the shared-media network; one or more of the one or more routing nodes are removed from the shared-media network; and a detection of one or more isolated nodes in the shared-media network.