We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks with extra channels). Instead, the model is based on analyzing the directions in which packets can turn in a network and the cycles that the turns can form. Prohibiting just enough turns to break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive for the network. In this paper, we focus on the two most common network topologies for wormhole routing, n-dimensional meshes and k-ary n-cubes, without extra channels. In an n-dimensional mesh, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns permit partial adaptiveness in routing. Partially adaptive routing ...

. Improvement of message latency and network utilization in torus interconnection networks by increasing adaptivity in wormhole routing algorithms is studied. A recently proposed partially adaptive algorithm and four new fully-adaptive routing algorithms are compared with the well-known e-cube algorithm for uniform, hotspot, and local traffic patterns. Our simulations indicate that the partially adaptive northlast algorithm, which causes unbalanced traffic in the network, performs worse than the nonadaptive e-cube routing algorithm for all three traffic patterns. Another result of our study is that the performance does not necessarily improve with full-adaptivity. In particular, a commonly discussed fully-adaptive routing algorithm, which uses 2 n virtual channels per physical channel of a k-ary n-cube, performs worse than e-cube for uniform and hotspot traffic patterns. The other three fully-adaptive algorithms, which give priority to messages based on distances traveled, perform ...

Chaotic routers are randomizing, non-minimal adaptive packet routers designed for use in the communication networks of parallel computers. Chaotic routing is reviewed along with other contemporary network routing approaches, including the state-of-the-art oblivious routers. Each routing approach is evaluated for its effectiveness as a multicomputer message router. The results indicate that the Chaos router is the most effective of known routing methods. 1 Introduction In spite of the fact that network routing has been an active research area in recent years, leading to many diverse proposals, practical experience with routers is extremely limited. The routers used in most implemented parallel computers are all from a single class, known as oblivious routers. Most of the non-oblivious routers have appeared only in single instance machines such as the HEP, CM-2, and CM-5 computers, making it difficult to separate fundamental properties of the routers from artifacts of the specific insta...

Wormhole routing has emerged as the most widely used switching technique in massively parallel computers. We present here a detailed survey of various techniques for enhancing the performance and reliability of the wormhole routing schemes in directly connected networks. We start with an overview of the direct network topologies and a comparison of various switching techniques. Next, the characteristics of wormhole routing mechanism are described in detail along with the theory behind deadlock-free routing. The performance of routing algorithms depends on the selection of path between the source and the destination, the network traffic, and the router design. The routing algorithms are implemented in the router chips. We outline the router characteristics and describe the functionality of various elements of the router. Depending on the usage of paths between the source and the destination, the routing algorithms are classified as deterministic, fully adaptive, and partially adaptive. ...

We present an adaptive deadlock-free routing algorithm which decomposes a given network into two virtual interconnection networks, V IN 1 and V IN 2 . V IN 1 supports deterministic deadlockfree routing, and V IN 2 supports fully-adaptive routing. Whenever a channel in V IN 1 or V IN 2 is available, it can be used to route a message. Each node is identified to be in one of three states: safe, unsafe, and faulty. The unsafe state is used for deadlock-free routing, and an unsafe node can still send and receive messages. When nodes become faulty/unsafe, some channels in V IN 2 around the faulty/unsafe nodes are used as the detours of those channels in V IN 1 passing through the faulty/unsafe nodes, i.e., the adaptability in V IN 2 is transformed to support fault-tolerant deadlock-free routing. Using information on the state of each node's neighbors, we have developed an adaptive fault-tolerant deadlock-free routing scheme for n-dimensional meshes and hypercubes with only two virtual channe...

Most machines of the last generation of distributed memory parallel computers possess specific routers which are used to exchange messages between non-neighboring nodes in the network. Among the several technologies, wormhole routing is usually prefered because it allows low channel-setup time, and reduces the dependency between latency and inter-node distance. However, wormhole routing is very susceptible to deadlock because messages are allowed to hold many resources while requesting others. Therefore, designing deadlock-free routing algorithms using few hardware facilities is a major problem for wormhole-routed networks. In this paper, we describe a general theoretical framework for the study of deadlockfree routing functions. We give a general definition of what can be a routing function. This definition captures many specific definitions of the literature (e.g., vertex-dependent, input-dependent, source-dependent, path-dependent, etc.). Using our definition, we give a necessary an...

: We present three protocols defining the relationship between messages and the channel resources requested: request-then-hold, requestthen -wait, and request-then-relinquish. Based on the three protocols, we develop an adaptive deadlockfree routing algorithm called the 3P routing. The 3P routing uses shortest paths and is fully-adaptive, so messages can be routed via any of the shortest paths from the source to the destination. Since it is a minimal or shortest routing, the 3P routing guarantees the freedom of livelocks. The 3P routing is not limited to a specific network topology. The main requirement for an applicable network topology is that there exists a deterministic, minimal, deadlock-free routing algorithm. Most existing network topologies are equipped with such an algorithm. In this paper, we present an adaptive deadlock-free routing agorithm for n-dimensional meshes by using the 3P routing. The hardware required by the 3P routing uses only one extra virtual channel as comp...

An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlock-free adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that can be used for any adaptive or nonadaptive routing algorithm for wormhole routing, as long as only local information is required for routing. The underlying proof technique introduces a new type of dependency graph, the channel waiting graph, which omits most channel dependencies that cannot be used to create a deadlock configuration. The necessary and sufficient condition can be applied in a straightforward manner to most routing algorithms. This is illustrated by proving deadlock freedom for a partially adaptive nonminimal mesh routing algorithm that does not require virtual channels and a fully adaptive minimal hypercube routing algorithm with two virtual channels per physical channel. B...

In this paper, we present a new concept of region of adaptivity with respect to various routing algorithms in wormhole networks. Using this concept, we demonstrate that the previously proposed routing algorithms, though more adaptive, cause an uneven workload in the network, which limits the performance improvement. It is observed that balanced distribution of traffic has greater impact on system performance than the adaptivity or efficiency of the algorithm. Based on these motivating factors, We have presented a new fully adaptive routing algorithm for 2-dimensional meshes using one extra virtual channel. The algorithm is more efficient in terms of the number of paths it offers between the source and the destination and also distributes the network load more evenly and symmetrically. The simulation results are presented and are compared with the results of previously proposed algorithms. It is shown that the proposed algorithm results in much better performance in terms of the average...

Multiprocessor interconnection networks based on low dimensional mesh or torus topologies and employing wormhole switching have become increasingly popular. Two concepts that have been proposed to improve the performance of such networks are Virtual Channel Flow Control (VCFC) and adaptive routing. Some previous studies have, however, found the latter technique to yield disappointing performance under uniform traffic patterns, while in this work we show that the former technique may result in degraded performance under certain non-uniform traffic patterns. This paper studies the interaction between VCFC and adaptive routing. It is shown that each of these techniques may yield unsatisfactory performance only when used in isolation, and that through their appropriate combination uniformly improved performance can be achieved. The consistent performance improvement and the magnitude of the performance improvement in some cases offers compelling motivation for implementing a combination of VCFC and adaptive routing in future machines. 1