On computing half-duplex relaying capacity in networks with orthogonal channels

We consider computing the capacity of half-duplex relay networks with orthogonal channels. In such networks, if the network has a layered structure, we show that the capacity can be computed in polynomial using the ellipsoid method. Moreover, for networks with local connectivity, such that the connectivity radius is a constant independent of size of the network, a polynomial time algorithm is presented to compute the capacity.