k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh

Rajasekaran, Sanguthevar

doi:10.1006/jagm.1995.1042

Cited by 24 publications

(12 citation statements)

References 26 publications

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“…For h n , column-sort performs poorly, because the operations in subnetworks are costly, while on a mesh, they are free. On a mesh, the randomized algorithm inspired by [22] also performs optimally [14], [8], because there the worst-case time consumption is determined by the time the packets need to cross the bisection. For the sparsemesh, this argument does not apply, and our deterministic routing algorithm is twice as fast.…”

Section: Resultsmentioning

confidence: 99%

Solving fundamental problems on sparse-meshes

Sibeyn¹

2000

IEEE Trans. Parallel Distrib. Syst.

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AbstractÐA sparse-mesh, which has PUs on the diagonal of a two-dimensional grid only, is a cost effective distributed memory machine. Variants of this machine have been considered before, but none are as simple and pure as a sparse-mesh. Various fundamental problems (routing, sorting, list ranking) are analyzed, proving that sparse-meshes have great potential. It is shown that on a two-dimensional n Â n sparse-mesh, which has n PUs, for h 3n Á log n, h-relations can be routed in h oha steps. The results are extended for higher dimensional sparse-meshes. On a d-dimensional n Â Á Á Á Â n sparse-mesh, with h 3n Á log n, h-relations are routed in T Á d À Ia À R Á h oh steps.

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Section: Resultsmentioning

confidence: 99%

Solving fundamental problems on sparse-meshes

Sibeyn¹

2000

IEEE Trans. Parallel Distrib. Syst.

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“…Numerous papers have been written on routing and sorting on the conventional mesh (see e.g., [30,28,11,14,12,25,26,24,22,7]). An excellent reference for algorithms on the conventional mesh is Leighton [13].…”

Section: Previous and New Resultsmentioning

confidence: 99%

Mesh connected computers with fixed and reconfigurable buses: packet routing and sorting

Rajasekaran

1996

IEEE Trans. Comput.

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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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“…The indexing scheme assumed is the blockwise snake-like row major indexing (which is the same as the scheme assumed in Refs. [6,7,19]). More details follow.…”

Section: Randomized Sortingmentioning

confidence: 97%

Permutation Routing and Sorting on the Reconfigurable Mesh

Rajasekaran

Mckendall

1998

Int. J. Found. Comput. Sci.

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In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation which we call as M r . We also make use of the standard PARBUS model. We show that permutation routing problem can be solved on a linear array M r of size n in |n steps, whereas n -1 is the best possible run time without reconfiguration. A trivial lower bound for routing on M T will be |. On the PARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal. We also show that permutation routing on an n x n reconfigurable mesh M T can be done in time n + o(n) using a randomized algorithm or in time 1.25n + o(n) deterministically. In contrast, 2n -2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n-2 steps on a conventional mesh. A lower bound of j is in effect for routing on the 2D mesh M r as well. On the other band, n is a lower bound for routing on the PARBUS and our algorithms have the same time bounds on the PARBUS as well. Thus our randomized routing algorithm is optimal upto a lower order term. In addition we show that the problem of sorting can be solved in randomized time n + o(n) on M T as well as on PARBUS. Clearly, this sorting algorithm will be optimal on the PARBUS model. The time bounds of our randomized algorithms hold with high probability.

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k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh

Cited by 24 publications

References 26 publications

Solving fundamental problems on sparse-meshes

Solving fundamental problems on sparse-meshes

Mesh connected computers with fixed and reconfigurable buses: packet routing and sorting

Permutation Routing and Sorting on the Reconfigurable Mesh

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