Recently proposed irregular networks can reduce the latency for both on-chip and off-chip systems with a large number of computing nodes and thus can improve the performance of parallel applications. However, these networks usually suffer from deadlocks in routing packets when using a naive minimal path routing algorithm. To solve this problem, we focus attention on a lately proposed theory that generalizes the turn model to maintain the network performance with deadlock-freedom. The theorems remain a challenge of applying themselves to arbitrary topologies including fully irregular networks. In this paper, we advance the theorems to completely general ones. Moreover, we provide a feasible implementation of a deadlock-free routing method based on our advanced theorem. Experimental results show that the routing method based on our proposed theorem can improve the network throughput by up to 138 % compared to a conventional deterministic minimal routing method. Moreover, when utilized as the escape path in Duato's protocol, it can improve the throughput by up to 26.3 % compared with the conventional up*/down* routing.

Network throughput has become an important issue for big-data analysis on Warehouse-Scale Computing (WSC) systems. It has been reported that randomly-connected inter-switch networks can enlarge the network throughput. For irregular networks, a multi-path routing method called k-shortest path routing is conventionally utilized. However, it cannot efficiently exploit longer-than-shortest paths that would be detour paths to avoid bottlenecks. In this work, a novel routing method called k-optimized path routing to achieve high throughput is proposed for irregular networks. We introduce a heuristic to select detour paths that can avoid bottlenecks in the network to improve the average-case network throughput. Experimental results by network simulation show that the proposed k-optimized path routing can improve the saturation throughput by up to 18.2% compared to the conventional k-shortest path routing. Moreover, it can reduce the computation time required for optimization to 1/2760 at a minimum compared to our previously proposed method.