A method of routing data in a multi-hop network. In one embodiment, the method includes: determining that a link-flow vector representing a set of flows to be routed from a source to a destination node satisfies necessary scheduling conditions for achievability; generating a scheduling multi-graph having at least one pair of nodes with multiple edges therebetween; deriving one or more sufficient scheduling conditions for achievability of the vector; solving a linear optimization problem over the necessary scheduling conditions to obtain an upper bound on achievability of the vector; and generating, based on the scheduling multi-graph, a routing solution that is a lower bound on the achievability of the vector and has a set of routes and associated schedule for achieving the vector. At least one node v receives transmissions from a specified plurality .OMEGA.(v) of other nodes. At least one of the scheduling conditions depends on .OMEGA.(v).