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.

....from low load to saturation. On the other hand, we have considered three kinds of message distribution: uniform, with locality, and specific. In the first case, message destination is randomly chosen among all the nodes. This pattern has been widely used in other performance evaluation studies [11, 8, 7]. For the message distribution with locality, the destination node is uniformly distributed inside a cube with side two centered at the source node, modeling short distance traffic. Finally, we have considered specific communication patterns between pairs of nodes. These patterns have been ....

A. 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, May 1992.

.... 1) virtual channels are needed for physical channel. For k ary n cubes with bidirectional links, 2 n Gamma1 virtual channels are needed 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 [6] 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 ....

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

....Routing Planar Adaptive Routing (PAR) is a limited adaptivity routing algorithm. PAR has many implementation advantages, most notably hardware simplicity. PAR uses only three virtual channels for deadlock prevention and small crossbar switches regardless of the number of dimensions [8, 21, 4]. The idea in planar adaptive routing is to provide limited adaptivity by routing adaptively in a series of two dimensional planes. As the packet progresses towards its destination, it passes through a series of adaptive planes and eventually, the packet completes routing in all dimensions and is ....

....the message header and generates requests for the permissible paths; trivial for a planar adaptive router. The RD arbitrates between simultaneous requests and enforces resource constraints (no more than one packet connected to each output) Our RD design uses the straight first selection policy [21] when there is no contention, giving the packets going straight priority over those turning. Fair arbitration is used to prevent starvation when a packet has already been forced to wait. 3.6 Switching A router must switch the packets, conveying data from appropriate inputs to outputs. This is ....

J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. Master's thesis, University of Illinois, Department of Electrical and Computer Engineering, January 1993.

....cannot form a cycle. This can be achieved by restricting the routing such as in the Turn model [16] or by splitting the traffic into two or more virtual channels so that cyclic dependencies are eliminated [10] There are multiple proposals of adaptive wormhole routers based on these approaches [21, 8]. Common drawbacks of these proposals are the high hardware complexity of the resulting device and the unbalanced use of the link resources. A second approach is deadlock recovery. When a deadlock situation is detected, one or more messages are removed so that the cycle is broken, allowing the ....

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

....is no previous work in applying adaptivity to configure a cache assist memory. However, adaptivity has been applied in various forms. Selected examples of its use are: 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. Adaptive throttling for interconnection networks [3] 16] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network behavior. Adaptive cache control of ....

Andrew A. Chien and Jae H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proc. 19th Annual Symposium on Computer Architecture, pages 268--277, 1992.

....1) virtual channels are needed for physical channel. For k ary n cubes with bidirectional links, 2 n Gamma1 virtual channels are needed 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 [7] 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 ....

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

....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 ....

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

....and across applications. Adaptivity is not a new concept in computer systems and has been applied before in various forms. Selected examples of its use are: ffl Adaptive routing pioneered by ARPANET in computer networks and, more recently, applied to multiprocessor interconnection networks [3, 5] to avoid congestion and route messages 1 faster to their destination; ffl Adaptive traffic throttling for interconnection networks [5] 15] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network behavior; ffl Adaptive cache ....

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

.... are cost effective facilities to alleviate the blocking [2] 8] 9] Nevertheless, a number of virtual channels still cost too much to accept [7] So one of the technical trends of wormhole routed interconnection networks is to find high performance designs using fewer virtual channels [2] [6] [13] 19] 20] The adaptive routing algorithm has been proved important in fully utilizing the virtual channel resources [13] However, among the much effort to search for adaptive routing algorithms with fewer virtual channels, relatively little has emphasized the load balance. In a previous ....

....used for messages to cross dimensions. That is, messages are routed plane by plane; on each plane, 2D VBMAR is used. Having set up this framework, we then enhance its overall adaptivity. We now describe the algorithm from these aspects. Planar routing The planar adaptive routing was proposed in [6] as a cost effective algorithm for n D meshes. It is also based on the CDG theory. According to the algorithm, a message is routed adaptively in a series of 2D planes. As the message progresses towards its destination, the routing dimensions change. Planes are traversed in a strictly decreasing ....

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

....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. ....

....The Dally and Aoki algorithms require a more complex router. Also, these algorithms require a header field in each message to record the number of dimension reversals suffered. The number of virtual channels assumed in their experiments (16 per physical channel) is also quite high. Chien and Kim [5] propose a partially adaptive algorithm called the planar adaptive algorithm that requires only a constant number of virtual channels independent of network size and dimension. This algorithm allows messages to be routed on a series of two dimensional adaptive planes. Within each adaptive plane, ....

A.A. Chien and J.H. Kim, "Planar-Adaptive Routing: Low-cost Adaptive Networks for Multiprocessors", Proceedings of the 19th Annual Symposium on Computer Architecture, May 1992, pp. 278-287.

....than the sector size and 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 [5], 7] to avoid congestion and route messages faster to their destination. ffl Adaptive throttling for interconnection networks [7] 18] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network 5 Program Input Instr Memory Name (M) ....

Andrew A. Chien and Jae H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proc. 19th Annual Symposium on Computer Architecture, pages 268--277, 1992.

....this communication pattern each node sends messages only to the node that has the reversed bit string as identifier. The negative impact of the internal conflicts can be alleviated by adaptive algorithms. Several examples already exists for the more common topologies, as the class of k ary n cubes [91, 7, 62, 13, 17, 27, 38, 48, 57, 64, 104]. Alternatively, interconnection topologies can be provided with many redundant paths and simpler routing algorithms [44] But this kind of solution is more expensive in terms of wiring complexity. External conflicts are the result of a poor program development or compilation process. An external ....

....are needed for physical channel. For k ary n cubes with bidirectional links, 2 n Gamma1 virtual channels are needed per physical link in each direction, if the network has no wrap around links (mesh connected) With wrap around links, the number increases to (n 1)2 n Gamma1 . Chien and Kim [27] 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 ....

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

....within and across applications. Adaptivity is not a new concept in computer systems and has been applied before in various forms. Selected examples of its use are: Adaptive routing pioneered by ARPANET in computer networks and, more recently, applied to multiprocessor interconnection networks [3, 4] to avoid congestion and route messages faster to their destination. Adaptive traffic throttling for interconnection networks [4] 16] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network behavior. Adaptive cache control or ....

A. Chien and J. Kim, Planar Adaptive Routing: Low-cost Adaptive Networks for Multiprocessors, Intl. Symposium on Computer Architecture, pp. 268-277, July 1992. 26

....is no previous work in applying adaptivity to configure a cache assist memory. However, adaptivity has been applied in various forms. Selected examples of its use are: 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. Adaptive throttling for interconnection networks [3] 16] shows that optimal limit varies and suggests admitting messages into the network adaptively based on current network behavior. Adaptive cache control of ....

Andrew A. Chien and Jae H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proc. 19th Annual Symposium on Computer Architecture, pages 268--277, 1992.

....(i.e. point to point) channels. The routing algorithm can be deterministic, such as the XY routing used in 2D meshes and the Dimension Order routing used in high dimensional meshes and hypercubes. It can be partially adaptive such as the Planar Adaptive routing proposed by Chien and Kim [ChienKim 92] or the West First and other similar algorithms that use the Turn Model of Glass and Ni [GlassNi 92] The routing algorithm can be fully adaptive, such as routing based on the concept of Virtual Networks [LinderHarden 91] or based on the concept of Dimension Reversal [DallyAoki 93] The routing ....

A. A. Chien and J. H. Kim, "Planaradaptive routing: Low-cost adaptive networks for multiprocessors", Proceedings of the 19 th International 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 ....

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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.

....packetization on two types of routers. First, we examine packetization in dimension order routers, similar to those in most existing multicomputer networks. Second, we extend our study to next generation networks which are likely to incorporate advanced routing techniques such as adaptive routing [12, 2] and virtual lanes 3 Chittor and Enbody studied the Symult 2010 system[13] in which long messages are split into packets of 256 bytes. 7] The remainder of the paper is organized as follows. In Section 2, we describe the simulation models and metrics used for the exploration. In Section 3, ....

....impact of packetization on the performance of advanced routing networks. 4 Packetization and Multipath Networks Several routing techniques that eliminate the intermessage interference in wormholerouted networks have been proposed. For example, multipath routing techniques such as adaptive routing [12, 2] and virtual lanes [7] reduce intermessage interference by circumnavigating congestion and multiplexing resources respectively. In this section, we investigate the impact of packetization on the advanced routing networks which incorporate both adaptive routing and virtual lanes. In such networks, ....

[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 Symposium on Computer Architecture, pages 268--77, May 1992.

....This allows messages to circumvent blocked messages, again, reducing the coupling between messages. Thus, the reduced coupling due to adaptivity should reduce the negative impact of long messages on network performance. The adaptive router we use is a planar adaptive router, described in detail in [8, 20]. However, its details are not important, as for the two dimensional networks in the simulations 2 , the planaradaptive router is a fully adaptive, minimal router. 3 Experimental model 3.1 Traffic model Actual multicomputer traffic loads consist of messages of a variety of different sizes, ....

A. Chien and J. Kim. Planar-Adaptive Routing: LowCost Adaptive Networks for Multiprocessors. In Proceedings of the International Symposium on Computer Architecture, May 1992.

....routers. Keywords: Multicomputers, Interconnection Networks, Adaptive Routing, Packet Routing, Parallel Processing, Transmission Order Preservation, Fault Tolerance Preliminary versions of some of this work appeared in the Proceedings of the 19th International Symposium on Computer Architecture [7] and the 4th Symposium on Parallel and Distributed Processing [22] Planar Adaptive Routing 2 1 Introduction In concurrent computers, interconnection networks are used by the processing nodes to exchange data and synchronize with each other. Network performance is often critical, as the ....

A. A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proceedings of the International Symposium on Computer Architecture, pages 268--77, May 1992.

....achievable clock period for the DOR to 9:8ns, only 16 faster the planar adaptive router. 5 The Cost of Adaptivity In this section, we characterize the cost of adaptivity by examining router designs with a range of adaptivity. These routers are all taken from the class of f flat adaptive routers [9]. The f flat adaptive routing framework can be used with any deadlock free adaptive routing algorithm within each f flat; we assume a Linder Harden router [25] with fully adaptive minimal routing. Increasing routing freedom not only increases the complexity of individual router modules, many more ....

A. A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. Journal of the Association for Computing Machinery, 1992. Revised Paper, Submitted for publication.

....produce poor performance for some communication patterns. Adaptive routing can alleviate such problems by mapping communications to paths flexibly, based on network loading. The flexibility in routing improves performance on non uniform workloads [22] and can provide a measure of fault tolerance [8]. The major disadvantage of adaptive routing is the greater complexity required to support the additional routing flexibility while assuring deadlock freedom. This increase in hardware complexity can significantly reduce router speed, decreasing total network performance. To reduce the cost of ....

....Routing Planar Adaptive Routing (PAR) is a limited adaptivity routing algorithm. PAR has many implementation advantages, most notably hardware simplicity. PAR uses only three virtual channels for deadlock prevention and small crossbar switches regardless of the number of dimensions [8, 21, 4]. The idea in planar adaptive routing is to provide limited adaptivity by routing adaptively in a series of two dimensional planes. As the packet progresses towards its destination, it passes through a series of adaptive planes and eventually, the packet completes routing in all dimensions and is ....

A. A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proceedings of the International Symposium on Computer Architecture, pages 268--77, May 1992.

....for building scalable high performance parallel machines. In order to minimize network latency, the current generation multicomputers employ wormhole (WH) switching technology [12] Fault tolerant routing in multicomputer networks is the subject of extensive research in recent years [3] 6] [8], 9] 11] 13] 15] 16] 21] 26] Chien and Kim[8] propose fault tolerant PAR(planar adaptive routing) algorithm in n dimensional mesh that is partially adaptive and uses 3 virtual channels per a physical channel. Chien and Kim s algorithm can tolerate anynumber of faults but a large ....

.... In order to minimize network latency, the current generation multicomputers employ wormhole (WH) switching technology [12] Fault tolerant routing in multicomputer networks is the subject of extensive research in recent years [3] 6] 8] 9] 11] 13] 15] 16] 21] 26] Chien and Kim[8] propose fault tolerant PAR(planar adaptive routing) algorithm in n dimensional mesh that is partially adaptive and uses 3 virtual channels per a physical channel. Chien and Kim s algorithm can tolerate anynumber of faults but a large number of functional processors may be deactivated to ensure ....

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

....requires a concrete cost and speed model. We instantiate our parametric model, using a 0.8 micron gate array technology and produce specific constants for all aspects of the model. This model is then used to compare a selection of routing algorithms: dimension order [14] planar adaptive [8], turn model [28] and channels [6] The comparison produces a variety of insights about the relative latency and achievable clock rate of these routers. In particular, we find that all of the adaptive routers we consider are significantly slower (longer setup latency and lower clock speeds) ....

....cycles which cause deadlock. A number of schemes have been developed which solve this problem [10, 28] 2.2 Adaptive Routing Adaptive routing has been proposed as a means of improving network throughput and performance robustness. A wide variety of adaptive routing algorithms have been proposed [24, 12, 16, 8, 28, 6]. However to date, most evaluations of adaptive routing algorithms use register transfer level simulation which shows how adaptive routing increases channel utilization but cannot measure the impact of additional router complexity on network latency and bandwidth. Adaptive routing allows paths to ....

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A. A. Chien and J. H. Kim. Planar-adaptive routing: Low-cost adaptive networks for multiprocessors. In Proceedings of the International Symposium on Computer Architecture, pages 268--77, May 1992.

....in order traffic is delivered in sequence, while the other packets arrive in unspecified order. In all cases, the planar adaptive networks are both deadlock and livelock free. Extended features of planar adaptive routing such as fault tolerance and in order transmission are described in detail in [1]. In this paper, we focus on the performance of the basic planar adaptive router in multi dimensional meshes (k ary n cubes without wraparounds) We assume wormhole routing [4] throughout the paper. In the following sections, we first briefly describe the planar adaptive routing (PAR) algorithm. ....

A. Chien and J. Kim. Planar-Adaptive Routing: LowCost Adaptive Networks for Multiprocessors. In Proceedings of the International Symposium on Computer Architecture, May 1992.

No context found.

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.

No context found.

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.

No context found.

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

No context found.

CHIEN, A. A., and KIM, J. H.: `Planar-adaptive routing: low-cost adaptive networks for multiprocessors', Journal of ACM, 1995, 42 (1), pp. 91-123

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