An incremental network topology for contention-free and deadlock-free routing

Wormhole switching has become the most widely used switching technique for multicomputers. However, the main drawback of wormhole switching is that blocked messages remain in the network, prohibiting other messages from using the occupied links and buffers. To address the deadlock problem without compromising communication latency and the incremental expansion capability that irregular networks can offer, we propose a simple topology called extended incremental triangular mesh (EITM) for switch-based networks. EITM is an extension of a previous ITM (incremental triangular mesh) topology with a more flexible structure. We also show that EITM is highly scalable, allows incremental expansion of systems, has guaranteed deadlock freedom, and can support contention-free multicast. First, we show that for an EITM, any shortest path routing method will not deadlock, therefore EITM networks are ideal for the escape paths in adaptive routing networks. Second, we show that it is possible to arrange the nodes of an EITM in a circular order so that two messages from independent parts of the circular order will not interfere with each other - this is extremely useful for implementing contention-free multicast and other collective communication operations. We also present the results on the relation between ITM/EITM, outer planar graphs and chordal graphs. We show that chordal graphs are strongly related to the freedom of deadlock for shortest path routing, and ITM in our previous paper is indeed maximum outer planar graph.