This article presents a reconfigurable network-on-chip architecture called ReNoC, which is intended for use in general-purpose multiprocessor system-on-chip platforms, and which enables application-specific logical NoC topologies to be configured, thus providing both efficiency and flexibility. The article presents three novel algorithms that synthesize an application-specific NoC topology, map it onto the physical ReNoC architecture, and create deadlock-free, application-specific routing algorithms. We apply our algorithms to a mixture of real and synthetic applications and target three different physical architectures. Compared to a conventional NoC, ReNoC reduces power consumption by up to 58% on average.