Problem This paper studies the problem of finding the optimal route of a stream between the transmitter and the receiver in an ad hoc network while minimizing the total power consumption. The main step of this work is modeling the transmissions as a graph, deduce the associated optimization problem and find a way to solve it. Compared to previous approaches, we introduce more flexibility by allowing the stream to be split between several intermediate destinations, and we do not use the specific approximations (mainly high SNR) required to make the problem convex. We illustrate our work using the following example where transmitions are splitted into two different channel to model the equivalent of downlink and uplink at each node. We call this graph ζ Source 12 5 1 Sink 9 3 8 subset 1 subset 2 2 11 10 7 6 4 The routing constraint The data flow model we use to express the routing constraint could be expressed. E.R E = S Where E is the incidence matrix of the graph and S the source sink vector. This formualtion lead to express R E as a function of less but free variables. R E = M.R E cT