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<p><b>Abstract</b>—System area networks (SANs), which usually accept arbitrary topologies, have been used to connect hosts in PC clusters. Although deadlock-free routing is often employed for low-latency communications using wormhole or virtual cut-through switching, the interconnection adaptivity introduces difficulties in establishing deadlock-free paths. An up*/down* routing algorithm, which has been widely used to avoid deadlocks in irregular networks, tends to make unbalanced paths as it employs a one-dimensional directed graph. The current study introduces a two-dimensional directed graph on which adaptive routings called left-up first turn (L-turn) routings and right-down last turn (R-turn) routings are proposed to make the paths as uniformly distributed as possible. This scheme guarantees deadlock-freedom because it uses the turn model approach, and the extra degree of freedom in the two-dimensional graph helps to ensure that the prohibited turns are well-distributed. Simulation results show that better throughput and latency results from uniformly distributing the prohibited turns by which the traffic would be more distributed toward the leaf nodes. The L-turn routings, which meet this condition, improve throughput by up to 100 percent compared with two up*/down*-based routings, and also reduce latency.</p>
Adaptive routing, deadlock avoidance, turn model, irregular topologies, system area networks, interconnection networks, PC clusters.

M. Koibuchi, H. Amano and A. Jouraku, "An Effective Design of Deadlock-Free Routing Algorithms Based on 2D Turn Model for Irregular Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 18, no. , pp. 320-333, 2007.
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