D. D. Chinn, T. Leighton, and M. Tompa. Minimal adaptive routing on the mesh with bounded queue size. In Proceedings of the 1994 ACM Symposium on Parallel Algorithms and Architectures, Cape May, NJ, June 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....new algorithm, i.e. we remove only the pure condition in this paper. Note that this# N) lower bound is quite tough; it still holds even without the oblivious condition; the destination exchangeable strategy also implies the same lower bound if the queue size is bounded above by some constant [4]. Our new bound can be extended to the case of general queue size k, namely, it is shown that there is an O(N 0.75 # k) algorithm for 2D, # N # N meshes of queuesize k, and there is an O(N 5 6 # k) algorithm for 3D, N 1 3 N 1 3 N 1 3 meshes of queue size k, while an # N k(8k) 5k ) ....

....k = 2 such that the sorted sequence x s is finally placed on the right half of the linear array, i.e. Pn 1 through P 2n finally hold x s1 through x sn in this order. Proof: The basic idea of the following oblivious algorithm is very similar to the idea implemented to adaptive routing in [4]: i) We first move those n packets to the right in nearest first order. That means the leftmost processor Pn 1 of the right half linear array receives packets in nearest first order, i.e. Pn 1 first receives the nearest packet x sn , next the second nearest packet x sn 1 and so on. ii) Then we ....

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D.D. Chinn, T. Leighton and M. Tompa, "Minimal adaptive routing on the mesh with bounded queue size," J. Parallel and Distributed Computing 34 (1996) 154-170.

....minimal adaptive algorithms, in which packets are allowed to choose a suitable path depending on the presence of other packets, but are still routed along a shortest path. Chinn, Leighton and Tompa analyze minimal adaptive routing of permutations on n Theta n meshes, with maximal queue size Q [11]. They prove a lower bound of O(n 2 =Q 2 ) for a large class of such algorithms. On the other hand, they present a minimal adaptive algorithm that solves the problem in O(n) steps with constant Q. The off line permutation routing problem on MIMD meshes has been considered by Kaklamanis, ....

Chinn, D.D., T. Leighton, M. Tompa, `Minimal Adaptive Routing on the Mesh with Bounded Queue Size,' Proc. 6th Symposium on Parallel Algorithms and Architectures, pp. 354--363, ACM, 1994.

....of all redundancy in the network to deliver messages regardless of faulty network components. We present extensions of the basic network to include multiple wire, multiple bit, and bidirectional wire support, as well as describing basic methods of using the EBN for various applications. ffl [Chinn et al. 94] UW CSE 94 07 04.PS) An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around hot spots. Minimal adaptive routing ....

....its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around hot spots. Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. Chinn, Leighton, and Tompa [Chinn et al. 94] provide a lower bound for permutation routing problems on the n 2 n mesh for a large class of deterministic minimal adaptive algorithms. Specifically, they prove that for any such routing algorithm, there exists a permutation that requires Omega# n 2 =k 2 ) steps to route all the packets in ....

D. D. Chinn, T. Leighton, and M. Tompa. Minimal adaptive routing on the mesh with bounded queue size. Technical Report UW-CSE-94-07-03, University of Washington, July 1994.

....b, running in O(bn) time In all hot potato routing algorithms, packets may take a detour. The algorithms are such that packets which have to go further make fewer detours, and therefore the overall completion time is close to optimal. However, individual packets may get delayed considerably. In [42] it is shown that such a flexibility is essential; lower bounds are constructed for adaptive routing algorithms which use routing of packets along shortest paths. Such algorithms are called minimal adaptive routing algorithms. For an n Theta n mesh, with maximal storage capacity k in each node, ....

Chinn, D. D., Leighton, T. and Tompa, M. Minimal adaptive routing on the mesh with bounded queue size. Proc. 6th ACM Symp. Parallel Alg. Arch. 1994, pp. 354--363.

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D. D. Chinn, T. Leighton, and M. Tompa. Minimal adaptive routing on the mesh with bounded queue size. In Proceedings of the 1994 ACM Symposium on Parallel Algorithms and Architectures, Cape May, NJ, June 1994.

....bound of Chapter 2. Chapter 4 describes a series of experiments on nonminimal adaptive algorithms and gives the results, which suggest that perhaps none of those discussed can route arbitrary permutations in O(n) time. A preliminary version of portions of Chapters 2 and 3 has appeared previously [CLT94] A preliminary version of portions of Chapter 4 has also appeared previously [Chi] This chapter concludes by surveying some of the known results for permutation routing. 1.1 Routing with Unbounded Queues Borodin and Hopcroft [BH85] prove an Omega Gamma p N=d 3=2 ) time bound for routing ....

D. D. Chinn, T. Leighton, and M. Tompa. Minimal adaptive routing on the mesh with bounded queue size. In Proceedings of the 1994 ACM Symposium on Parallel Algorithms and Architectures, Cape May, NJ, June 1994.

....destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around hot spots. Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. Chinn, Leighton, and Tompa [6] provide a lower bound for permutation routing problems on the n Theta n mesh for a large class of deterministic minimal adaptive algorithms. Specifically, they prove that for any such routing algorithm, there exists a permutation that requires Omega (n 2 =k 2 ) steps to route all the ....

....poor performance. On the n Theta n mesh, there theoretically is enough bandwidth to deliver all packets in any permutation in time proportional to n. At the very least, a good routing algorithm should be able to route permutations efficiently (i.e. in O(n) time) Chinn, Leighton, and Tompa [6] (hereafter referred to as CLT) show that for any algorithm in a large class of deterministic minimal adaptive algorithms for the n Theta n mesh, there exists a permutation for that algorithm such that it takes Omega (n 2 =k 2 ) steps to route all packets in the permutation, where k is the ....

D. D. Chinn, T. Leighton, and M. Tompa. Minimal adaptive routing on the mesh with bounded queue size. In Proceedings of the 1994 ACM Symposium on Parallel Algorithms and Architectures, Cape May, NJ, June 1994.

....closer to its destination. For instance, the greedy algorithm with FIFO queueing discipline is destination exchangeable, but the algorithms based on sorting are not. Destination exchangeability is an attempt to characterize the simplicity of the queueing discipline. Chinn, Leighton, and Tompa [6] show that any deterministic, minimal, destination exchangeable routing algorithm on the n 2 n mesh requires Omega# n 2 =q 2 ) steps to route some permutation, where q is the queue size. Note that the sorting based algorithms are neither minimal nor destinationexchangeable, which is why ....

D. D. Chinn, T. Leighton, and M. Tompa. Minimal adaptive routing on the mesh with bounded queue size. In Proceedings of the 1994 ACM Symposium on Parallel Algorithms and Architectures, Cape May, NJ, June 1994.

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