Sorting n Numbers on n × n Reconfigurable Meshes with Buses

Nigam, M.; Sahni, Sartaj

doi:10.1006/jpdc.1994.1117

Cited by 28 publications

(12 citation statements)

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“…An equally impressive amount of work has been done on the mesh with reconfigurable buses as well (see e.g., [2,16,17,31,18]). …”

Section: Previous and New Resultsmentioning

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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“…An equally impressive amount of work has been done on the mesh with reconfigurable buses as well (see e.g., [2,16,17,31,18]). …”

Section: Previous and New Resultsmentioning

confidence: 99%

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

Rajasekaran

1993

Algorithms—ESA '93

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“…Rather remarkably, our sorting algorithm requries only 35 broadcasts, a substantial improvement over the 59 broadcasts required by the algorithm of Nigam and Sahni [20].…”

Section: Preliminariesmentioning

confidence: 98%

“…The purpose of this section is to sorting algorithm on a model similar to the reconfigurable mesh and consisting of layered n ϫ n reconfigurable meshes. Later, Nigam and Sahni [20] proposed a more efficient implementation of column-sort that requires only 59 broadcasts.…”

Section: Preliminariesmentioning

confidence: 99%

“…Although the running time of the algorithm is O(1), a more accurate measure of its complexity is provided by the number of broadcast operations required by the algorithm [20]. The best performance of a sorting algorithm known to date involves 59 broadcasts [20].…”

Section: The Bucket Sort Algorithm-implementation Detailsmentioning

confidence: 99%

“…The reconfigurable mesh combines two desirable features of massively parallel architectures, namely, nearly constant diameter and a dynamically reconfigurable bus system. It is not surprising, therefore, that the sorting problem has received a great deal of attention in the context of reconfigurable architectures [4,7,9,11,13,16,17,19,20,22,23,27,29]. In an early paper, Wang et al [29] proposed a constant-time sorting algorithm on a three-dimensional reconfigurable mesh, using O(n 3 ) processors.…”

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confidence: 97%

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