Interference management has become a key factor in regulating transmissions in wireless communication networks. To support effective interference management schemes, it can be essential to have prior knowledge about the network topology. In this paper, we build on existing results in the literature on the simulation of the message passing model, and present an efficient strategy for fast discovery of the network topology during a pilot communication phase. More precisely, we investigate the minimum number of communication rounds that is needed to discover an arbitrary network topology with a maximum number of links per receiver, while assuming a single-hop network that is restricted to interference-avoidance based schemes in its pilot phase. We first ignore any interference cancellation strategy such that no receiver can recognize, and cancel transmissions of, previously discovered transmitters, and then capture the gains obtained through interference cancellation during the pilot phase. Our results evince how the required number of rounds scale in an approximately logarithmic fashion with practical values of the total number of users in the network, having a slope proportional to the number of interfering transmitters per receiver.