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A technique to enhance multicomputer routers for faulttolerant routing with modest increase in routing complexity and resource requirements is described. This method handles solid faults in meshes, which includes all convex faults and many practical nonconvex faults, for example, faults in the shape of L or T. As examples of the proposed method, adaptive and nonadaptive faulttolerant routing algorithms using four virtual channels per physical channel are described.

We show that deadlocks due to dependencies on consumption channels are a fundamental problem in wormhole multicast routing. This type of resource deadlocks has not been addressed in many previously proposed wormhole multicast algorithms. We also show that deadlocks on consumption channels can be avoided by using multiple classes of consumption channels and restricting the use of consumption channels by multicast messages. We provide upper bounds for the number of consumption channels required to avoid deadlocks. In addition, we present a new multicast routing algorithm, column-path, which is based on the well-known dimension-order routing used in many multicomputers and multiprocessors. Therefore, this algorithm could be implemented in existing multicomputers with simple changes to the hardware. Using simulations, we compare the performance of the proposed column-path algorithm with the previously proposed Hamiltonian-path-based multipath and an e-cube-based multicast routing algorithms. Our results show that for multicast traffic, the column-path routing offers higher throughputs, while the multipath algorithm offers lower message latencies. Another result of our study is that the commonly implemented simplistic scheme of sending one copy of a multicast message to each of its destinations exhibits good performance provided the number of destinations is small.

Abstract-This paper presents a framework to design fully-adaptive, deadlock-free wormhole algorithms for a variety of network topologies. The main theoretical contributions are (a) design of new wormhole algorithms using store-and-forward algorithms, (b) a sufficient condition for deadlock free routing by the wormhole algorithms so designed, and (c) a sufficient condition for deadlock free routing by these wormhole algorithms with centralized flit buffers shared among multiple channels. To illustrate the theory, several wormhole algorithms based on store-and-forward hop schemes are designed. The hop-based wormhole algorithms can be applied to a variety of networks including torus, mesh, de Brujin, and a class of Cayley networks, with the best known bounds on virtual channels for minimal routing on the last two classes of networks. An analysis of the resource requirements and performances of a proposed algorithm, called negative-hop algorithm, with some of the previously proposed algorithms for torus and mesh networks is presented.

W e show that deadlocks due to dependencies on consumption channels is a fundamentalproblem an multicast wormhole routing. This issue of deadlocks has not been addressed in many previously proposed multicast algorithms. We also show that deadlocks on consumption channels can be avoided by using multiple classes of consumption channels and restricting the use of consumption channels by multicast messages. In addition, we present a new multicast routing algorithm, column-path, which uses the well-known e-cube algorithm for multicast routing. Therefore, this algorithm could be implemented in the existing multicomputers with minimal hardware support. W e present a simulation study of the performance of Hamilton-path based multicast algorithms with the proposed co!umn-path algorithm. Our simulations indicate that the simplistic scheme of sending one copy of a multicast message to each of its destinations exhibits good performance and that the new column-path algorithm offers higher throughput compared to the Hamilton-path based algorithms.