Scheduling in omnidirectional relay networks

We consider the optimal scheduling problem of the omnidirectional relay scheme in wireless networks. In a half-duplex model, we first present an optimal operation scheme that can achieve the maximum rate for the all-source all-cast problem for both one-dimensional and two-dimensional regular networks. Then, we show that the same rate can also be achieved with the greedy scheme. In the full-duplex model, the maximum rate is achieved with a simpler proof compared to the previous result. Some discussions are presented on more general networks.