A. Chien and J. H. Kim. Planar-adaptive routing: lowcost adaptive networks for multiprocessors. Journal of ACM, 42(1):91--123, Jan. 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....allow packets to create a cyclic dependence. A deadlock occurs when packets in a cyclic dependence chain cannot make forward progress and hold on to resources, such as buffer space, that other packets in the chain require to make forward progress. Some solutions, such as partially adaptive routing [5, 13], trade performance for deadlock freedom by limiting the algorithm s routing options to eliminate the possibility of deadlock cycles. Other solutions, such as deadlock avoidance [10] and deadlock recovery [18] can be thought of as consisting of two logical networks: one fully adaptive network and ....

A. A. Chien and J. H. Kim. Planar-Adaptive Routing: Low-cost Adaptive Networks for Multiprocessors. In Proceedings of the 19th Annual International Symposium on Computer Architecture, pages 268--277, May 1992.

....used, for instance, in tailoring the interaction of processing with I O, customization of CPU elements (e.g. splittable ALU resources) etc. Architectural adaptation is not a new idea. Adaptive routing pioneered by ARPANET in computer networks is applied to multiprocessor interconnection networks [3] to avoid congestion and route messages faster to their destination. Adaptive traffic throttling for interconnection networks [13] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network behavior . Adaptive cache control or coherence ....

A. Chien and J. Kim. Planar adaptive routing: low-cost adaptive networks for multiprocessors. In Int'l Symp. Computer Architecture, pages 268--277, 1992.

....than the sector size, then only a fraction of the cache will hold valid data. Adaptivity has also been applied in other forms. Selected examples of its use are: ffl Adaptive routing pioneered by ARPANET in computer networks and, more recently, applied to multiprocessor interconnection networks [1, 3], to avoid congestion and route messages faster to their destination. ffl Adaptive throttling for interconnection networks [3] 14] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network behavior. ffl Adaptive cache control or ....

A. Chien and J. Kim. Planar adaptive routing: low-cost adaptive networks for multiprocessors. In Int'l Symp. Computer Architecture, pages 268--277, 1992.

....and selection functions combine with a set of destination distributions to determine network performance. While other studies have looked at comparing various routing algorithms over different patterns, most studies limit the selection functions used [14 16] the range of algorithms evaluated [7, 10, 17], or the destination distributions considered [11, 18] 3 Distribution Description NodeUniform Uniform random selection of destination node MatrixTranspose Source (x; y) selects destination (y; x) BitComplement Destination node id is the bit complement of the source id BitReversal ....

A. A. Chien and J. H. Kim, "Planar-adaptive routing: Low-cost adaptive networks for multiprocessors," Journal of the ACM, vol. 42, pp. 91--123, January 1995.

....and selection functions combine with a set of destination distributions to determine network performance. While other studies have looked at comparing various routing algorithms over different patterns, most studies limit the selection functions used [14 16] the range of algorithms evaluated [7, 10, 17], or the destination distributions considered [11, 18] Distribution Description NodeUniform Uniform random selection of destination node MatrixTranspose Source (x, y) selects destination (y,x) BitComplement Destination node id is the bit complement of the source id BitReversal Destination ....

A. A. Chien and J. H. Kim, "Planar-adaptive routing: Low-cost adaptive networks for multiprocessors," Journal of the ACM, vol. 42, pp. 91 123, January 1995.

....a mesh does not have any wrap around channels. Routing algorithms for only mesh topologies are reviewed here, because wormhole routing has been used primarily on low dimension meshes and the focus of this paper is on mesh topologies. Many adaptive routing algorithms for meshes have been proposed [2, 3, 5, 8, 9, 10, 11]. Table 1 summarizes the main features of each algorithm. VCs is used as an abbreviation for number of virtual channels. Designing deadlock free routing algorithms for wormhole routing was simplified by a proof that an acyclic channel dependency graph guarantees deadlock freedom [6] Each node of ....

.... as functions of the form R: C x N C, where the incoming channel, belonging to the set of channels C, and the destination node, belonging Table 1: Overview of Adaptive Routing Algorithms for Meshes Author(s) Fully VCs for Comments Adaptive 2D Mesh Partially Adaptive for Chien Kim [2] Yes 6 Higher Dimensions Daily [3] Yes 6 2D Mesh Only Daily Aoki [5] Yes 2D Mesh with x nodes Glass Ni [8] Yes 6 2D Mesh Only Glass Ni [9] No 4 Roughly Half the Adaptiveness of Fully Adaptive Jesshope, Miller Yes 8 Number of Virtual Yantchev [10] Channels is Exponential Linder Harden [11] ....

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A. A. Chien and J. H. Kim. Planar-Adaptive Routing: Low-cost Adaptive Networks for Multiprocessors. In Proceedings of the 19 ; Annual International Symposium on Computer Architecture, pages 268 277, 1992.

....to implement and deadlock free. However, it does not make effective use of all communication links in a system. Fully adaptive algorithms [9] allow a mes sage to be routed along any of the shortest paths from the source to the destination processor Partially adap tive algorithms like planar [3] restrict routing freedom to two dimensions at a time. Figure 1 illustrates the differences between these three routing schemes. Higher adaptivity has poten tial to reduce link contention and hence is useful to reduce the overall execution time of a given program. However, for any of the above ....

A. A. Chien and J. H. Kim, "Planar-Adaptive Routing: Low-Cost Adaptive Networks for Multiprocessors, " In International Symposium on Computer Architecture, pp. 268-277, 1992.

....simple to implement and deadlock free. However, it does not make effective use of all communication links in a system. Fully adaptive algorithms [11] allow a message to be routed along any of the shortest paths from the source to the destination processor. Partially adaptive algorithms like platar [4] restrict routing freedom to two dimensions at a time. Figure 2 illustrates the differences between these three routing schemes for a 3 dimensional cube. Higher adaptivity has potential to reduce link contention and hence is useful to reduce the overall execution time of a given program. However, ....

A. A. Chien and J. H. Kim. Planar Adaptive Routing: Low-cost Adaptive Networks for Multipro- cessors. In 19th Annual International Symposium on Computer Architecture, pages 268 277, May 1992.

....low latency and less requirement of buffer storage. However, this accompanies with high probability of channel contention or even deadlock. Researchers have proposed schemes using virtual channels for increasing physical channel utilization [5] exploiting adaptivity [6, 16] and avoiding deadlock [2, 4, 6, 16]. Routing algorithms to avoid deadlock are also investigated in [8] Multicast represents the most complex communication pattern. It is in general NP complete and remains so even with some restrictions [10, 13] Heuristics based on finding a multicasting tr ee from a source node have been ....

....22 and 25. With the above conditions, one can easily see that excluding the faulty nodes, the network remains connected. A linear path can be constructed on the mesh from left to right by including as many nodes as possible using a greedy strategy. For example, in Fig. 4(a) one possible path is [1, 2, 4, 3, 5, 7, 8, 10, 12, 14, 13, 15, 16, 18, 17, 19, 21, 23, 24, 26, 28, 27, 29, 30, 32, 31]. This path is 26 nodes long, with only 2 healthy nodes un routed. In general, no more than f healthy nodes will be unused and the path length is 2 2f. The readers are requested to refer to [1] for the embedding procedure. Lemma 4 [1] In an n cube with f ( k(nd 1) 2] faulty nodes, the e ....

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A. A. Chien and J. H. Kim, "Planar-adaptive Routing: Low-cost Adaptive Networks for Multiprocessors," Int'l Syrup. on Computer Architecture, 1992, pp. 268-277.

....oblivious routing. Simulation experiments are performed with all to one pattern and randomly generated non uniform traffic to study the interplay. Through simulation experiments we determine the factor of improvement in latency with multiple consumption channels under oblivious, planar adaptive [2], and fully adaptive [7] routing schemes. Using non uniform traffic we demonstrate the latency throughput behavior of various network configurations by varying the number of consumption channels and routing schemes. 2 Characterizing Consumption Bottleneck The effects of the consumption ....

....can proceed concurrently with S4. Figure l(b) also shows the respective message latencies with VCFC. VCFC and adaptive routing techniques use virtual channels for improved flow control and deadlock prevention, respectively. With the performance improvement suggested by adaptive routing algorithms [2, 8], future systems are more likely to support adaptive routing using virtual channels. Additional use of virtual channels for flow control (VCFC) is less likely to be used due to cost and technological constraints. 0,0) 1,0) 2,0) 3,0) 4,0) si 4 4 4 s 13 7 13 ss 17 11 6 Figure h An ....

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A. A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proc. of the Int'l Symp. on Comp. Architecture, pp. 268d77, May 1992.

....directly affect link contention and hence completion time of a parallel application. Deterministic (also known as e cube or oblivious) routing [4] allows a message to take a fixed path from a given source to its destination. On the other hand, adaptive routing strategies (partially adaptive [3] and fully adaptive [7] permit messages to take alternate paths while avoiding the busy links. Such adaptivity has potential to reduce link contention between messages conflicting emporally and spaially over some common links. While the distributed memory systems are undergoing the above ....

....degree of adaptive hess from partially to fully adaptive. Fully adaptive algorithms allow a message to be routed along any of the shaortest paths from the source to the destination processor while partially adaptive algorithms restrict routing freedom. Figure lb shows planar routing proposed in [3] which limits routing freedom to two dimensions at a time. It is thus partially adaptive for topologies with dimension greater than 2. Figure lc shows how fully adaptive routing [7] can provide more edge disjoint paths between two processors. Higher adaptivity reduces message contentions and hence ....

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A.A. Chien and J.H. Kim, "Planar Adaptive Routing: Low-cost Adaptive Networks for Multiproces- sors," Proceedings of the 19th Annual Int. Sym. on Computer Architecture, May 1992, pp. 268-277.

....problem of deadlock is more serious in adaptive routing than in oblivious routing, because the constraints which prevented deadlock in dimension order oblivious routing are no longer present in minimal adaptive routing, so other techniques must be used to guarantee deadlock freedom. Some routers [10, 11] require extra buffering as well as extra constraints on possible paths for packets in order to prevent deadlock. Other routers [12, 13] are fully minimally adaptive. They allow all minimal paths, although some amount of extra buffering is still required. However, these algorithms require ....

Chien, A. A., and Kim, J. H. Planar-adaptive routing: Low-cost adaptive network for multiprocessors. Proc. 19th International Symposium on Computer Architecture. 1992, pp. 268--277.

....Barrier synchronization schemes in [6] are tuned towards iwarp system. The unicast based barrier synchronization for hypercubes [14] does not exploit the benefits of path based routing [11] on wormhole routed networks. Virtual channels are increasingly becoming popular to support adaptive routing [3] and increased throughput [5] It is feasible to dedicate a set of virtual channels in a network for the exclusive use of the synchronization traffic. This provides the flexibility and raises new challenges to develop synchronization schemes for systems supporting wormhole routing and ....

....networks supporting path based routing. Using this primitive, we propose two schemes: distancebased and synchronization worm based. The distance based scheme can use either single or multiple paths. This is designed for wormhole networks supporting deterministic and minimaladaptive routing [3]. The synchronization worm based scheme extends the scope to networks supporting fully adaptive routing. The rendezvous primitive is proposed for both wormhole routed networks not supporting path based routing and circuit switched networks [7] The proposed schemes are generic and they can work ....

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A. A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In lnt'l Symposium on Computer Architecture, pages 268 277, 992.

....For example, Linder and Harden [13] describe fully adaptive minimal algorithms for k ary n cubes that require 2 n Gamma1 virtual channels per physical link in each direction, if the network has no wrap around links. With toroidal cubes the number increases to (n 1)2 n Gamma1 . Chien and Kim [4] presented an approach to trade off adaptivity against the number of virtual channels. Their algorithm, called planar adaptive routing, is minimal and partially adaptive. This approach involves examining the routing dimensions in pairs, and constraining the routing choices at any time to one or ....

A. A. Chien and J. K. Kim. Planar Adaptive Routing: LowCost Adaptive Networks for Multiprocessors. In Proceedings of the 19th Annual Symposium on Computer Architecture, pages 268--277, May 1992.

....networks is one of the factors discouraging its use in commercial massively parallel machines. Most existing adaptive routing algorithms guarantee deadlock freedom by defining cycle free routes on a set of virtual networks implemented with virtual channels. Cycles can be prevented statically [1, 2, 3, 4] or dynamically [5, 6] Unfortunately, virtual channels can be expensive because they complicate routing decision and channel control, increasing router node delay significantly [7] Consequently, to achieve adaptive routing with speed comparable to dimension order routers, more efficient adaptive ....

....a number of researchers have developed algorithms to reduce the number of virtual channels required for deadlock prevention in mesh networks. Chien and Kim developed planar adaptive routing which requires a constant number (three) of virtual channels regardless of network size and dimension [3]. Duato developed a theory of deadlock free adaptive routing which dynamically prevents deadlock while using only two virtual channels [5] Sanz et al. developed the channels routing algorithm which is based on the same concept. In addition, Ni and Glass have developed a unique approach to ....

[Article contains additional citation context not shown here]

A. A. Chien and J. H. Kim, "Planar-adaptive routing: Low-cost adaptive networks for multiprocessors," in Proceedings of the International 5'ymposium on Computer Architecture, pp. 268 77, May 1992.

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A. Chien and J. H. Kim. Planar-adaptive routing: lowcost adaptive networks for multiprocessors. Journal of ACM, 42(1):91--123, Jan. 1995.

No context found.

A. A. Chien and J. H. Kim. Planar-adaptive routing: LowCost adaptive networks for multiprocessors. Journal of the ACM, 42(1):91--123, 1995.

No context found.

A.A. Chien and J.H. Kim, "Planar-adaptive routing: Low-cost adaptive networks for multiprocessors," Proc. 19th Ann. Int'l Symp. Computer Architecture, pp. 268--277, May 1992.

No context found.

A. A. Chien and J. H. Kim. Planar-adaptive routing: LowCost adaptive networks for multiprocessors. Journal of the ACM, 42(1):91--123, 1995.

No context found.

A. A. Chien and J. H. Kim. Planar-adaptive routing: LowCost adaptive networks for multiprocessors. Journal of the ACM, 42(1):91--123, 1995.

No context found.

A. A. Chien and J. H. Kim. Planar-adaptive routing: LowCost adaptive networks for multiprocessors. Journal of the ACM, 42(1):91--123, 1995.

No context found.

A. A. Chien and J. H. Kim. Planar-adaptive routing: LowCost adaptive networks for multiprocessors. Journal of the ACM, 42(1):91--123, 1995.

No context found.

A. A. Chien and J. H. Kim. Planar-adaptive routing: LowCost adaptive networks for multiprocessors. Journal of the ACM, 42(1):91--123, 1995.

No context found.

A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proceedings of the 19th International Symposium on Computer Architecture, pages 268#277, 1992.

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A. A. Chien and J. Kim, Planar Adaptive Routing: Low-Cost Adaptive Networks for Multiprocessors, Journal of ACM vol. 42, no. 1, pp. 91-123, 1995.

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