Efficient coloring of Wireless Ad Hoc Networks with diminished transmitter power

In our work we present a new approach to the problem of channel assignment in Wireless Ad Hoc Network. We introduce a new algorithm which works in distributed model of computations on Unit Disc Graphs modeling the Wireless Ad Hoc Network. The algorithm first modifies the transmitting power of the devices constituting the network (radii of the vertices of the Unit Disc Graph) and then it assigns the frequencies in the network adjusted to our demands. We assume that initially all the devices have the same transmission range and we are able to reduce the transmission range of some of them in order to decrease the number of necessary frequencies. We are able to diminish the number of communication links without loosing connectivity of the network, i.e. reduce the number of possible interference threats without risk of loosing possibility to exchange information. In addition, the diminution of communication range reduce the power consumption of the transmitting devices.