In this paper, we study a wireless network that has constant or slow-varying data rate requirements. The transmitters transmit to multiple receivers. The allocation of degrees of freedom (orthogonal codes, spectrum or time-slots) is based on a weight vector that is associated with each transmitter. The weight vector will specify how the degrees of freedom should be shared between the receivers associated with the transmitter. This model applies not only to the downlink of a cellular network, but also to more general wireless networks, including multi-hop networks. We devise two distributed algorithms in order to determine the minimal power allocation for the transmitters that will meet the data rate requirement between each transmitter-receiver pair. The main feature of our algorithms is that they can be executed at each transmitter independently with local information.