L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are cost effective facilities to alleviate the blocking [8] 9] 4] Nevertheless, a number of virtual channels still cost too much to accept. So one of the technical trends of wormhole routed interconnection networks is to find high performance designs using less virtual channels [16] 23] 7] [20] [14] Adaptive routing algorithm has been proved important in fully utilizing the virtual channel resources [16] An adaptive routing algorithm actually consists of two parts, a routing function and a selection function [10] The routing function supplies a set of routable paths, and the ....

....of routing algorithms [11] The selection function forbids use of some virtual channels when the load is below a certain threshold. Simulations show that it can lead good performance for his family of algorithms. Schwiebert compared a number of routing policies for the opt y routing algorithm [20], and identified the best policy for the algorithm [21] In fact, many authors have tried to optimize the routing policy implicitly in their routing algorithm design [16] 23] 14] 20] These routing policies are specific to certain routing algorithms. Feng evaluated three commonly used routing ....

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L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes, Proceedings of Supercomputing'93, pp. 782-791, 1993.

....channels. Their fully adaptive minimal routing algorithm for n D meshes uses 2 n 1 virtual channels. It became clear shortly later that so many virtual channels are impractical from cost and complexity [7] Much effort was then made to find cost effective schemes with fewer virtual channels. In [17] the opt y routing algorithm was proposed using two virtual networks. Messages are allowed to travel across virtual networks on some certain conditions. However, the conditions are too strict, and are asymmetric for different virtual networks. In [20] the authors paid special attention on load ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes, Proceedings of Supercomputing'93, pp. 782-791, 1993.

....advantage of. Messages have several routing choices at each node and the path choices are made based on the local information available at the node. Adaptive routing can help in increasing the achievable network throughput [9, 10, 11] Many new routing schemes have been proposed in recent research [3, 5, 8, 10, 12, 13, 16]. A detailed survey of various routing schemes in wormhole networks can be found in [14] One disadvantage of adaptive routing in wormhole networks, however, is that it increases the likelihood of deadlocks. Thus, preventive measures have to be taken in the routing algorithm to avoid deadlocks. ....

L. Schwiebert and D.N. Jayasimha, "Optimal Fully Adaptive Wormhole Routing for Meshes", Proceedings of Supercomputing

....2.4 Deadlock Deadlock is another important consideration in designing a network system, and one that has been the subject of numerous studies. Various avoidance techniques have been proposed, such as in Y in X in X out CPU M E M O R Y Routing Y out Buffers Flit Figure 1: Structure of a Node [LMN93, SS93, CK92, GN92b, SJ93, LH91, LGS92]. In general, deadlock avoidance is achieved either by restricting routing or by the addition of hardware such as virtual channels, as proposed in [DS87] A recent study describing a new model of deadlock freedom can be found in [Dua93] The issue of deadlock, however, is orthogonal to that of ....

L. Schwiebert and D. N. Jayasimha. Optimal fully adaptive wormhole routing for meshes. In Proc. Supercomputing `93, pages 782--791, November 1993.

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L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

....router means that the message can choose either of the two channels going along X out of that router. The effect of adaptivity on average and standard deviation of latencies has been studied by using partially adaptive (for example, West first [9] and fully adaptive (for example, Opt y [13]) routing algorithms. West first has roughly half the adaptiveness of a fully adaptive routing algorithm. Opt y has been proved to be optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels [13] 6 Simulation Setup ....

....adaptive (for example, Opt y [13] routing algorithms. West first has roughly half the adaptiveness of a fully adaptive routing algorithm. Opt y has been proved to be optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels [13]. 6 Simulation Setup Simulation has been used to evaluate the different approaches described in previous sections. We have varied the message length, message generation frequency, traffic pattern and routing algorithm to see how well the different approaches work with different values of these ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

....and output buffer to the physical channel. 28 channels [8] so fewer virtual channels are usually better. In general, the less adaptive a routing algorithm, the more modest the virtual channel requirements, however, this is not always the case. For example, some fully adaptive routing algorithms [88] require fewer virtual channels than some partially adaptive routing algorithms [9] Reducing the number of virtual channels needed for a given degree of adaptiveness is accomplished by using a less restrictive routing algorithm. Conversely, when the same number of virtual channels is used, a less ....

....as the Intel Paragon and the Symult 2010. Consequently, many adaptive routing algorithms have been developed for meshes. Although we discuss many mesh routing algorithms in detail, we first present a brief overview in Table 1 of the routing algorithms for meshes that were known when our result [88] was first published. In Table 1, VCs is used as an abbreviation for number of bidirectional virtual channels per router. Glass and Ni [40, 42] used the turn model methodology to propose several partially adaptive routing algorithms for meshes. One example, negative first, first routes a message ....

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L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

....hypercubes, any routing algorithm for arbitrary dimension meshes or tori can be extended to hypercubes, since an n dimensional hypercube is a special case of an n dimensional mesh or torus. Only a few fully adaptive routing algorithms have been designed for n dimensional mesh and torus topologies [1, 8, 21, 24, 27, 28]. When restricted to hypercubes, the routing algorithms proposed by Jesshope, Miller, and Yantchev [21] and by Linder and Harden [24] require more virtual channels than the routing algorithm proposed by Duato [11] The routing algorithm proposed by Dally and Aoki [8] is more restrictive than ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

....edge in the channel dependency subgraph defines a direct dependency. An indirect dependency is a dependency between two channels in the subgraph that exists only because of the intermediate use of one or more channels not in the subgraph. This methodology has been used by Schwiebert and Jayasimha [26] to propose a fully adaptive minimal routing algorithm for meshes. Berman, et al. 1] propose a torus routing algorithm with a routing relation of the form R : C Theta N Theta N C p that allows cyclic dependencies between the channels. Dally and Aoki [7] prove deadlock freedom for a routing ....

....hypercubes, any routing algorithm for arbitrary dimension meshes or tori can be extended to hypercubes, since an n dimensional hypercube is a special case of an n dimensional mesh or torus. Only a few fully adaptive routing algorithms have been designed for n dimensional mesh and torus topologies [1, 7, 20, 23, 26]. When restricted to hypercubes, the routing algorithms proposed by Jesshope, Miller, and Yantchev [20] and by Linder and Harden [23] require more virtual channels than the routing algorithm proposed by Duato [10] The routing algorithm proposed by Dally and Aoki [7] is more restrictive than the ....

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L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993. An extended version of this result to appear in the Journal of Parallel and Distributed Computing.

....in a timeshared manner. We consider the popular two dimensional mesh architecture and compare the performance of four representative mesh routing algorithms: Dimension order routing (using X Y) with two and three virtual channels per physical channel, Duato s mesh routing algorithm [5] and OptY [8]. The latter two algorithms are fully adaptive while dimension order routing is deterministic. With X Y routing using multiple virtual channels, the routing function still remains the same as for basic X Y routing in the sense that it decides, in a deterministic manner, whether the header should ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. Technical Report OSU-CISRC-4/93-TR16, The Ohio State University, 1993. Revised August 13, 1993.

....condition for deadlock free routing for adaptive routing algorithms defined by functions of the form R : N Theta N P(C) where the current node and the destination node, independent of the input channel, define the set of output channels on which to route the message. Schwiebert and Jayasimha [14, 16] have used Duato s sufficiency condition and the mesh topological properties to propose a fully adaptive routing algorithm for arbitrary dimension mesh networks that is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels. ....

SCHWIEBERT, L., AND JAYASIMHA, D. N. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93 (1993), pp. 782--791.

....wormhole routing algorithms that require an acyclic ordering of the channels. Duato [9, 11] proved that requiring an acyclic ordering of the channels is not necessary for adaptive routing algorithms if the output channel is selected independent of the input channel. Schwiebert and Jayasimha [27] have used Duato s proof technique to propose an optimal fully adaptive routing algorithm for meshes. Berman, et al. 1] prove deadlock freedom for a torus routing algorithm that has no acyclic ordering of the channels and allows the router to consider the input channel when selecting the output ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993. An extended version of this paper will appear in the Journal of Parallel and Distributed Computing.

....any restrictions, in the X dimension and in any direction using virtual channel two. The Optimal Fully Adaptive routing algorithm is fully adaptive and deadlock free for arbitrary dimension meshes. Furthermore, this algorithm uses only the minimum number of virtual channels. The proofs, given in [12], are extensions of the proofs for the 2D mesh. Limited research has been done on wormhole routing for higher dimension meshes. For example, mad y has been defined only for 2D meshes [8] The partially adaptive routing algorithm proposed by Glass and Ni in [9] while requiring no additional ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. Technical Report OSUCISRC -4/93-TR16, The Ohio State University, 1993.

....channel dependency graph. He also designed adaptive routing algorithms based on the relaxed condition. Schwiebert and Jayasimha have used Duato s sufficiency condition and the mesh topological properties to propose optimal fully adaptive routing algorithms for arbitrary dimension mesh networks [SJ93, SJ95b]. These algorithms are optimal in the number of virtual channels and in the number of restrictions they place on the use of virtual channels. A natural question that arises is: Exactly how restrictive must the routing algorithm be to guarantee deadlock freedom In other words, what is a necessary ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

....channels. Similarly, we show that changing the selection function can change the balance of traffic in the network and improve performance, even without changing the routing algorithm. Our simulations use a fully adaptive routing algorithm, called opt y, proposed by Schwiebert and Jayasimha [13, 14]. For n dimensional meshes, opt y has the fewest restrictions of any fully adaptive minimal routing algorithm for meshes, so opt y provides the maximum number of virtual channels for each message. By using opt y as the routing algorithm in our simulations, we maximize the flexibility of the ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

....extended channel dependency graph. He also designed routing algorithms based on this relaxed condition. Schwiebert and Jayasimha have used Duato s sufficiency condition and the mesh topological properties to propose an optimal fully adaptive routing algorithm for arbitrary dimension mesh networks [16, 18]. This algorithm is optimal in the number of virtual channels and in the number of restrictions they place on the use of virtual channels. A natural question that arises is: Exactly how restrictive must the routing algorithm be to guarantee deadlock freedom In other words, what is a necessary ....

L. Schwiebert and D. N. Jayasimha. Optimal Fully Adaptive Wormhole Routing for Meshes. In Supercomputing '93, pages 782--791, 1993.

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