Matching the bisection bound for routing and sorting on the mesh

Kaufmann, Michael; Rajasekaran, Sanguthevar; Sibeyn, Jop F.

doi:10.1145/140901.140905

Cited by 34 publications

(29 citation statements)

References 13 publications

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“…It requires 5knÂ4+o(kn) steps. Several improvements gradually reduced the routing time to almost optimal [141,158,263]. One of the most important ideas is packet coloring [158]; the packets are colored deterministically, or at random, white or black.…”

Section: On-line Routingmentioning

confidence: 99%

See 1 more Smart Citation

Packet Routing in Fixed-Connection Networks: A Survey

Grammatikakis

Hsu

Kraetzl

et al. 1998

Journal of Parallel and Distributed Computing

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Section: On-line Routingmentioning

confidence: 99%

“…This idea goes back to Valliant and Brebner [317]. Near-optimal results were first achieved with randomized algorithms [141,263]. It was then discovered that randomization is superfluous and can be replaced by sorting packets in submeshes and performing unshuffling [144,160].…”

Section: On-line Routingmentioning

confidence: 99%

Packet Routing in Fixed-Connection Networks: A Survey

Grammatikakis

Hsu

Kraetzl

et al. 1998

Journal of Parallel and Distributed Computing

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“…The algorithm used in [8] is nothing but Algorithm B. We could make use of the same algorithm to route on M r also.…”

Section: Thus Phase I (And Phase Iii) Can Be Completed Within Kn 12mentioning

confidence: 99%

Mesh connected computers with fixed and reconfigurable buses: Packet routing, sorting, and selection

Rajasekaran

1993

Algorithms—ESA '93

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Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing and sorting on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k − k routing and k − k sorting on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1 − 1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1 − 1 routing, k − k routing, and k − k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed * This research was supported in part by an NSF Research Initiation Award CCR-92-09260. Preliminary versions of some of the results in this paper were presented in the First Annual European Symposium on Algorithms, 1993. 1 in logarithmic time on a mesh with fixed buses. Most of our algorithms have considerably better time bounds than known algorithms for the same problems.

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“…Optimal algorithms for k-k routing and sorting are presented in [2,3,5,7]. The implementation of Valiant and Brebner's algorithm [8] which is given in [3], consists of four phases:…”

Section: Routing On Meshesmentioning

confidence: 99%

“…All algorithms considered in this paper consist of phases in which the routing is performed only in rows or columns (possibly one routing in the rows is overlaid with an independent routing in the columns). The time for such an operation on one-dimensional submeshes has been analyzed in detail in [2].…”

Section: Preliminariesmentioning

confidence: 99%

Better deterministic routing on meshes

Sibeyn

Proceedings 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing. IPPS/SP

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Optimal randomized and deterministic algorithms have been given for k-k routing on two-dimensional nn meshes. The deterministic algorithm is based on "column-sort" and exploits only part of the features of the mesh. For small n and moderate k, the lower-order terms of this algorithm make it considerably more expensive than the randomized algorithm. In this paper, we present a novel deterministic algorithm, which, by exploiting the topology of the mesh, has lowerorder terms that are almost negligible, even smaller than those of the randomized algorithm. An additional advantage of the new algorithm is that it routes average-case packet distributions twice as fast as worst-case distributions. In earlier algorithms this required additional steps for globally probing the distribution.

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Matching the bisection bound for routing and sorting on the mesh

Abstract: In this paper we present randomized algorithms for k-

Cited by 34 publications

References 13 publications

Packet Routing in Fixed-Connection Networks: A Survey

Packet Routing in Fixed-Connection Networks: A Survey

Mesh connected computers with fixed and reconfigurable buses: Packet routing, sorting, and selection

Better deterministic routing on meshes

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