R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. "Universal algorithms for store-and-forward and wormhole routing", Proc. of 28th STOC, pp. 356-365, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Low congested k IRS have been first considered in [2] and [17] Such an issue is crucial in parallel computation because good parallel model simulations and more in general efficient routing scheduling algorithms are strongly related to the congestion of the path system routed by the messages [3, 10, 15]. Besides its theoretical interest, the combination of congestion problems with interval routing is relevant also for parallel implementation, since k IRS have been used in the last generation of INMOS Transputer C104 Router chips together with wormhole routing [12] that is very sensitive to the ....

.... its theoretical interest, the combination of congestion problems with interval routing is relevant also for parallel implementation, since k IRS have been used in the last generation of INMOS Transputer C104 Router chips together with wormhole routing [12] that is very sensitive to the congestion [3, 10]. Finally, this devising goal is important also from a fault tolerance point of view, as a link failure should not disconnect too many source destination pairs. The congestion of the path systems induced by the (not necessarily interval) routing schemes has been extensively investigated in the ....

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 356--365, Philadelphia, Pennsylvania, 22--24 May 1996.

....as the maximum number of induced paths connecting pairs in R that share the same physical link. This issue is crucial in parallel and distributed architectures because the efficiency of the underlying routing strategy is strongly related to the congestion of the path system routed by the messages [24, 5, 19]. Besides its theoretical interest, the combination of congestion problems with interval routing is relevant also from an implementation point of view, since k IRS have been used in the last generation of INMOS Transputer C104 Router chips together with wormhole routing [22] In fact, the wormhole ....

....path routed by the message, L is the number of flits per message, and B is the channel bandwidth. Hence, if L is sufficiently large, the path length D does not significantly affect the transmission time. At the same time, as shown by several efficient scheduling routing protocols (see for instance [5, 19]) when more than one message is sent simultaneously, the transmission time becomes heavily dependent from the congestion of the used path system, i.e. by the maximum number of messages stepping through a same physical link. For instance, in [5] an algorithm has been proposed whose delivering time ....

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 356--365, Philadelphia, Pennsylvania, 22--24 May 1996.

....problem (studied in our paper and in, e.g. 15, 20] and A preliminary version of this paper was presented at the 8th International Symposium on Algorithms and Computation, ISAAC 97, under the title Competitive Source Routing on Tori and Meshes. 1 the scheduling problem (studied in, e.g. [9, 11, 12, 13, 16, 17]) The former concerns itself with assigning paths to packets, whereas the latter deals with deciding the order in which the packets along the prede ned paths are moved in order to resolve con icts if multiple packets are waiting for the same edge. Clearly the e ectiveness of an algorithm depends ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proceedings of the TwentyEighth Annual ACM Symposium on the Theory of Computing, pages 356-365, 1996.

....mesh, with maximal storage capacity k in each node, it is shown that for a large class of minimal adaptive routing algorithms there are inputs which require at least Omega Gamma n 2 =k 2 ) steps. The topics of wormhole and hot potato routing have been considered for more general networks in [54, 93, 215, 216, 268]. Particular attention is devoted to vertex symmetric networks (among them tori and butterflies) More practical aspects of wormhole routing, taking into account that not only the connections of the network have finite speed, but that also the rate with which the nodes can supply data to the ....

Cypher, R., Meyer auf der Heide, F., Scheideler, C. and Voking, B. Universal algorithms for store-andforward and wormhole routing. Proc. 28th ACM Symp. on Theory of Computing, 1996, pp. 356--365.

....protocol in [27] that the following result holds. Theorem 2.12 There is an online protocol for sending packets along an arbitrary path collection of size n with dilation D, congestion C and edge latency L in time O(C D log n) w.h.p. With a more involved proof that combines the ideas in [14] and [32] with Theorem 2.9, the following result can be shown. Theorem 2.13 There is an online protocol for sending packets along an arbitrary simple path collection of size n with dilation D, congestion C, maximum edge latency L and minimum edge latency in time O Gamma log(L= C (D L ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In 28th Ann. ACM Symp. on Theory of Computing, pp. 356-365, 1996.

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-andforward and wormhole routing. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 356--365, 1996.

No context found.

R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal algorithms for store-andforward and wormhole routing. In 28th Ann. ACM Symp. on Theory of Computing, pp. 356-365, 1996.

No context found.

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 356-365, 1996.

.... is an off line schedule for any simple (i.e. loop free) path collection with dilation D and congestion C that sends all packets along their paths (one packet per path) in time O(C D) Since then, many on line algorithms have been presented for various classes of path collections (see, e.g. [13, 16, 8, 21, 18]) To give two examples, in [8] Cypher et al. present an on line, buffer less algorithm that works for any simple path collection of size n. Their algorithm delivers all packets to their destinations in time O D log log n C log n log log n log log(C D) w.h.p. provided that the ....

....e. loop free) path collection with dilation D and congestion C that sends all packets along their paths (one packet per path) in time O(C D) Since then, many on line algorithms have been presented for various classes of path collections (see, e.g. 13, 16, 8, 21, 18] To give two examples, in [8] Cypher et al. present an on line, buffer less algorithm that works for any simple path collection of size n. Their algorithm delivers all packets to their destinations in time O D log log n C log n log log n log log(C D) w.h.p. provided that the communication links have a ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal algorithms for store-andforward and wormhole routing. In Proc. of the 28th ACM Symp. on Theory of Computing, pp. 356-365, 1996.

....III von Bund und Landern through the DAAD. This research was conducted in part while he was staying at the Heinz Nixdorf Institute, with support provided by the DFG Sonderforschungsbereich 376. 1 1 Introduction Many static routing protocols have been developed in recent years (see, e.g. [9, 8, 10, 13, 6, 12]) These protocols aim to route some initially given set of packets along predetermined paths in a network as fast as possible. In practice however, networks are rarely used in this static fashion but packets are injected dynamically into the network. Since much less is known in the area of ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-andforward and wormhole routing. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 356--365, 1996.

....simple path collection of size n with dilation D, congestion C, maximum edge latency L and minimum edge latency in time O log(L= C D log (L= Delta log n) L Delta log(n Delta L= log (L= Delta log n) 2 ; w.h.p. Proof. The proof basically combines the ideas in [14] and [32] with Theorem 2.12. Let us assume in the following that D L Delta n. The case D L Delta n can be dealt with similar to the proof of Theorem 2.13 (see the way the random rank protocol calls Route(s) Furthermore, let us assume for the moment that the minimum edge latency, is 1. We ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal algorithms for store-andforward and wormhole routing. In 28th Ann. ACM Symp. on Theory of Computing, pp. 356-365, 1996. 31

....III von Bund und Landern through the DAAD. This research was conducted in part while he was staying at the Heinz Nixdorf Institute, with support provided by the DFG Sonderforschungsbereich 376. 1 1 Introduction Many static routing protocols have been developed in recent years (see, e.g. [8, 7, 9, 12, 5, 11]) These protocols aim to route some initially given set of packets along predetermined paths in a network as fast as possible. In practice however, networks are rarely used in this static fashion but packets are injected dynamically into the network. Since much less is known in the area of ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 356--365, 1996.

....along an arbitrary simple path collection of size n with dilation D, congestion C, maximum edge latency L and minimum edge latency in time O log(L= C D log (L= log n) L log(n L= log (L= log n) 2 ; w.h.p. Proof. The proof basically combines the ideas in [14] and [33] with Theorem 2.12. Let us assume in the following that D L n. The case D L n can be dealt with similar to the proof of Theorem 2.13 (see the way the random delay protocol calls Route(s) Furthermore, let us assume for the moment that the minimum edge latency, is 1. We again ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal algorithms for store-andforward and wormhole routing. In 28th Ann. ACM Symp. on Theory of Computing, pp. 356-365, 1996.

....or distributed system is the efficient communication of data between processors. While it is possible to design a specific routing algorithm for each possible interconnection network, a much more general approach is to create a single universal routing algorithm that can be used in any network [22, 8]. In addition to providing a unified approach to routing in standard networks, universal routing algorithms are ideally suited to routing in irregular networks that are used in wide area networks and that arise when standard networks develop faults. Whereas several randomized online protocols for ....

....this protocol to design optimal randomized protocols for arbitrary node symmetric networks. Recently, Ostrovski and Rabani [29] found a randomized protocol for arbitrary simple path collections that runs in time O(C D log 1 n) w.h.p. for any constant 0, using buffers of size C . In [8], Cypher et al. present a randomized protocol for arbitrary simple path collections that runs in time O( D log log n C log n log log n log log(C D) log(C D) log log(C D) w.h.p. and requires buffers of size O( log(C D) log log(C D) Not many strategies for deterministic routing ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal Algorithms for Store-andForward and Wormhole Routing. In 28th Ann. ACM Symp. on Theory of Computing, pp. 356-365, 1996.

....among all network resources. This corresponds to minimizing the congestion, i.e. the maximum, taken over all links or buses, of the amount of data transmitted by the link or bus divided by the respective bandwidth. Known results for store and forward routing [9, 11, 14, 15] and wormhole routing [3, 4, 15] show that reducing the congestion is most important in order to get a good network throughput. For this reason, we believe that minimizing the congestion is a promising approach in order to develop data management strategies that work eciently in theory and practice. In [8] it is shown in an ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proceedings of the 28th ACM Symposium on Theory of Computing (STOC), pages 356-365, 1996.

....or links are the bottleneck in these systems, because improving communication bandwidth and latency is often more expensive or more difficult than increasing processor speed and memory capacity. But whereas several standard methods are known for hiding latency, e.g. pipelined routing (see, e.g. [14, 16]) redundant computation (see, e.g. 3, 4, 21, 26, 27, 28] or slackness (see, e.g. 32] the only way to bypass the bandwidth bottleneck is to reduce the communication overhead by exploiting locality. The theoretical analysis of the access tree strategy in [25] considers data management in a ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store--and--forward and wormhole routing. In Proc. of the 28th ACM Symp. on Theory of Computing (STOC), pages 356--365, 1996.

....C. Besides their off line result, Leighton, Maggs, and Rao present in [6] a simple on line scheduling protocol which completes the routing in time O(C D Delta log(DN ) w.h.p. and requires buffers of size log(DN ) A similar routing time but with much smaller buffer size is achieved in [3]: a protocol is given requiring routing time O(C D Delta log N ) w.h.p. using buffers of size log D. Better results are known for special classes of networks. For instance, Ranade [12] proposes a probabilistic on line routing protocol for butterfly networks. The proof is based on the delay ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal Algorithms for Store--and--Forward and Wormhole Routing. In Proceedings of the 28th Symposium on Theory of Computing, pp. 356--365, 1996.

....knowledge, nothing has been found out so far about the maximum number of trials to send a message to its destination given an arbitrary path collection with some fixed bandwidth, if wavelength conversion is not allowed. In case that wavelength conversion is allowed at every router, Cypher et al. [10] presented an online protocol that routes messages of length L along any simple path collection with congestion C and dilation D in time O( L Delta C Delta D 1=B (D L) log n) B) w.h.p. However, all optical devices for wavelength conversion are still a topic in research and might ....

....of a successful worm reaches its source, or the worm or its acknowledgement has been (partly) discarded. Note that if we use priority routers it can happen that worms are only partly discarded. Previously, only delay sequence arguments were used to analyze such protocols (see, e.g. [10, 30]) In this paper we use delay tree arguments that yield much more accurate upper bounds on the runtime. In particular, we are able to prove the following three results depending on the contention resolution rule. Their proofs can be found in Section 2 and Section 3. Let ff = C B( D L 1) 2 ....

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, B. Vocking. Universal Algorithms for Storeand -Forward and Wormhole Routing. To appear at 28th Ann. ACM Symp. on Theory of Computing, 1996.

....of the most relevant. Routing in Butterfly Networks. There is a vast literature on routing in butterfly networks [20, 21] Much of the early work focuses on store and forward routing [1, 23, 24, 31, 35, 39, 41, 42] More recently, there has been progress in analyzing wormhole routing algorithms [10, 11, 13, 36]. Since we present no new results in these two routing methods, we focus only on the butterfly circuitswitching literature. In two early papers, Beizer [8] and Benes [9] showed that any static permutation routing problem can be routed with congestion 1 and dilation 2 log n on an n input Benes ....

R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, May 1996.

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. "Universal algorithms for store-and-forward and wormhole routing", Proc. of 28th STOC, pp. 356-365, 1996.

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In STOC '96.

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. "Universal algorithms for store-and-forward and wormhole routing", Proc. of 28th STOC, pp. 356-365, 1996.

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for store-and-forward and wormhole routing. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 356-365, Philadelphia, Pennsylvania, 22-24 May 1996. 15

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. Universal algorithms for storeand -forward and wormhole routing. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 356-365, Philadelphia, Pennsylvania, 22-24 May 1996.

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R. Cypher, F. Meyer auf der Heide, C. Scheideler, and B. Vocking. "Universal algorithms for store-and-forward and wormhole routing", Proc. of 28th STOC, pp. 356-365, 1996.

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