The paper addresses the important issue related to communication performance of Networks on Chip (NoCs), namely the complexity of collective communications measured by a required number of algorithmic steps. Three NoC topologies are investigated, a ring network, Octagon and 2D-mesh, due to their easy manufacturability on a chip. The lower complexity bounds are compared to real values obtained by evolution-based optimizing tools. Results give hints on what communication overhead is to be expected in ring- and mesh-based NoCs with the wormhole switching, full duplex links and k-port noncombining nodes.