In the area of network performance and discovery, network tomography focuses on reconstructing network properties using only end-to-end measurements at the application layer. One challenging problem in network tomography is reconstructing available bandwidth along all links during multiple source/multiple destination transmissions. The traditional measurement procedures used for bandwidth tomography are extremely time consuming. We propose a novel solution to this problem. Our method counts the fragments exchanged during a BitTorrent broadcast. While this measurement has a high level of randomness, it can be obtained very efficiently, and aggregated into a reliable metric. This data is then analyzed with state-of-the-art algorithms, which correctly reconstruct logical clusters of nodes interconnected by high bandwidth, as well as bottlenecks between these logical clusters. Our experiments demonstrate that the proposed two-phase approach efficiently solves the presented problem for a number of settings on a complex grid infrastructure.