Deadlock-free Routing Algorithm Research Articles

Deadlock-free wormhole routing algorithms for star graph topology

For constructing massively parallel multicomputers with over 5000 processing nodes, the star graph topology is known to be better than the hypercube in terms of the average routing distance, the number of links per node, and the fault diameter. The authors present two deadlock-free algorithms for routing in star graph, assuming the wormhole routing model. Both the algorithms use the concept of virtual channels introduced by W. Dally and C.L. Seitz (1987). The first algorithm is non-optimal in terms of the average routing distance, but uses fewer virtual channels on the whole. The second algorithm is optimal in terms of routing performance, but requires a somewhat larger number of virtual channels per node.

Flexible Routing Criteria for Circuit-Switched Hypercubes

Circuit-switched communication has been increasingly used in hypercube multiprocessors. Reserve-and-hold strategy is commonly used to establish a circuit-switched path between a pair of nodes in the hypercube. With this strategy, a routing algorithm has to be designed with sufficient care to avoid deadlocks. A commonly used, deadlock-free routing algorithm for establishing a path between any two nodes in a hypercube is the e-cube routing algorithm. This algorithm is oblivious and allows only one shortest path between each source-destination pair and, hence, does not utilize the flexibility provided by the hypercube. In this paper, we propose a new set of routing criteria for circuit-switched hypercubes that exploit the flexibility provided by the hypercube. Our routing criteria are provably deadlock-free and route messages along shortest paths. The number of paths allowed by these criteria is more than one for most source-destination pairs. We show that the flexibility provided by our routing criteria can be used to limit the negative effects due to component failures. We derive the exact number of disrupted source-destination pairs in the presence of a single component failure. We then show that these numbers can be minimized using the proposed relabeling techniques. The performance of the routing criteria is evaluated using simulations. The results show that our criteria, if used effectively, lead to a significant improvement in performance over the e-cube routing strategy for non-uniform traffic. In addition, worst-case time complexity with respect to permutation routing is studied.

Performance analysis of mesh interconnection networks with deterministic routing

This paper develops detailed analytical performance models for k-ary n-cube networks with single-hit or infinite buffers, wormhole routing, and the nonadaptive deadlock-free routing scheme proposed by Dally and Seitz (1987). In contrast to previous performance studies of such networks, the system is modeled as a closed queueing network that: includes the effects of blocking and pipelining of messages in the network; allows for arbitrary source-destination probability distributions; and explicitly models the virtual channels used in the deadlock-free routing algorithm. The models are used to examine several performance issues for 2-D networks with shared-memory traffic. These results should prove useful for engineering high-performance systems based on low-dimensional k-ary n-cube networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

ON THE DESIGN OF DEADLOCK-FREE ADAPTIVE MULTICAST ROUTING ALGORITHMS

Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. Two multicast wormhole routing methods have been presented in [13] for multicomputers with 2D-mesh and hypercube topologies. Also, a theory for the design of deadlock-free adaptive routing algorithms for wormhole networks has been proposed in [7, 8]. This theory supplies the sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. This paper analyses the additional channel dependencies produced by multicast routing algorithms on wormhole networks. Then, the theory proposed in [7, 8] is extended by considering them. As an example, the multicast routing algorithms presented in [13] are extended, taking advantage of the alternative paths offered by the network.

CHANNEL CLASSES: A NEW CONCEPT FOR DEADLOCK AVOIDANCE IN WORMHOLE NETWORKS

In previous papers, we have developed the theoretical background for the design of deadlock-free adaptive routing algorithms for store-and-forward and wormhole networks. Some definitions and theorems have been proposed, developing conditions to verify that an adaptive algorithm is deadlock-free, even when there are cyclic dependencies between channels. Also, two design methodologies have been proposed. In this paper, we propose a partial order between channels as well as an equivalence relation. This relation splits the set of channels into equivalence classes. Then, we extend our previous theory by considering equivalence classes (channel classes) instead of channels. This extension drastically simplifies the verification of deadlock freedom for adaptive routing algorithms with cyclic dependencies between channels. Finally, we present an example.

Design, implementation and evaluation of a deadlock-free routing algorithm for concurrent computers

This paper describes the design, the implementation, and the performance results of a routing algorithm which provides deadlock-free communication in a tightly coupled message-passing concurrent computer. The algorithm is adaptive, isolated and uses the store-and-forward technique. It allows message communication between two processes regardless of where they are physically located on the network. The routing algorithm has many positive characteristics including provable deadlock freedom, guaranteed message arrival, and automatic local congestion reduction. It can be used as a basis for the design of high-level communication primitives. An Occam implementation on a network of inmos Transputers is discussed. The experimental results show that the routing algorithm is effective to support process to process communication on a concurrent computer.

Deadlock-free message routing in multicomputer networks

The execution of a concurrent computation by a network of processors requires a routing algorithm that is deadlock free. Many routing algorithms proposed for processor networks have the potential of deadlock due to the cyclic topology of the network. In this paper we first formalize the concept of message routing. Next, we show a method by which a deadlock-free routing algorithm can be constructed out of a given routing algorithm. Finally the method is illustrated by constructing deadlock-free routing algorithms for cartesian product processor networks.

Deadlock-Free Message Routing in Multiprocessor Interconnection Networks

A deadlock-free routing algorithm can be generated for arbitrary interconnection networks using the concept of virtual channels. A necessary and sufficient condition for deadlock-free routing is the absence of cycles in a channel dependency graph. Given an arbitrary network and a routing function, the cycles of the channel dependency graph can be removed by splitting physical channels into groups of virtual channels. This method is used to develop deadlock-free routing algorithms for k-ary n-cubes, for cube-connected cycles, and for shuffle-exchange networks.