The WK-recursive network well conforms to implementation of large distributed systems due to its many favorable properties. In this paper, we employ the concept S 3 group to establish an efficient look-ahead routing algorithm for the triplet-based WK-recursive network. Remarkably, we introduce a data flow model to categorize message traffic as six flow models. For the sake of simplicity, we further leverage the permutation group S 3 to transform different flow models to one model and hence

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... ng computing can be performed in the same model. It is demonstrated that our proposed design can achieve better network performance. The triplet-based WK-recursive network (TriBA) is a subclass of WK-recursive networks [1], which has many desirable properties such as symmetry, scalability and hierarchy. Whereas the network topology [2] determines the ideal performance of a network-on-chip (NoC), routing is one of the key factors that determines how much of this potential is realized [3] . An efficient routing algorithm [4, 5] renders hop counts of routed packets as few as possible, leading to reduce the overall network latency. Further, a well-designed routing mechanism has an important impact on how to optimize the router microarchitecture [6], e.g., look-ahead routing strategy [7] can be used to optimized the router pipeline stages, resulting in significantly reducing the communication delay. Previous studies have proposed a number of routing algorithms for TriBA, such as DDRA [8], Min-DDRA [9] and SPORT [10]. DDRA adopts the distributed routing, which computes the output port at each hop based on the relative position of the region in which the target node is located. However, it cannot always provide shortest-path for routing. Min-DDRA creates a routing table for every router to record the intermediate node to the other nodes. Although the shortest path is obtained, there exists a main disadvantage in this table-lookup deterministic routing algorithm. When a TriBA network expands to a larger scale, the routing tables must be updated. Moreover, the routing table stored in each node is more difficult to be obtained especially in large scale TriBA. SPORT is a source routing algorithm which uses recursion to predetermine complete routing path. The computational complexity is relative high. Moreover, the whole routing information should be attached on the head flit, leading to increase the packet size and decrease the network payload. In this paper, we propose an efficient look-ahead routing algorithm for TriBA NoC (LA4T) with the following attributes. Our proposal always routes the message along the minimal path. Unlike source routing algorithm, it adopt the distributed routing which selects the output port at each hop simply depend on the destination address, the size of the header routing information can be reduced, resulting increasing the network payload. Otherwise, it is orthogonal to the scale of the network and hence can be easily extended to different sizes of TriBA network. Further, with the constraint of shortest-path routing, the output port of the next hop can be easily reasoning. Route look-ahead can be applied to shorten the router pipeline stages. Such a scheme significantly cuts down packet latency and boosts throughput.