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Ethernet networks rely on the so-called spanning tree protocol (IEEE 802.1d) in order to break cycles, thereby avoiding the possibility of infinitely circulating packets and deadlocks. This protocol imposes a severe penalty on the performance and scalability of large gigabit Ethernet backbones, since it makes inefficient use of expensive fibers and may lead to bottlenecks. We propose a significantly more scalable cycle-breaking approach, based on the novel theory of turn-prohibition. Specifically, we introduce, analyze and evaluate a new algorithm, called tree-based turn-prohibition (TBTP). We show that this polynomial-time algorithm maintains backward-compatibility with the IEEE 802.1d standard and never prohibits more than 1/2 of the turns in the network, for any given graph and any given spanning tree. Through extensive simulations on a variety of graph topologies, we show that it can lead to an order of magnitude improvement over the spanning tree protocol with respect to throughput and end-of-end delay metrics. In addition, we propose and evaluate heuristics to determine the replacement order of legacy switches that results in the fastest performance improvement.