Sorting n numbers on n*n reconfigurable meshes with buses

The reconfigurable mesh is a parallel model of computation, which exploits a massive amount of rather simple processing elements connected through a reconfigurable interconnection network. During the last decades, the model received strong interest and many researchers have devised algorithms for it. However, most of this work focuses on theoretical aspects. Due to some idealistic modeling assumptions only a few attempts have been made to implement the model and to study the practical use of reconfigurable meshes. In this paper, we leverage the reconfigurable mesh model to study potential architectures and programming models for future many-cores. We design a reconfigurable mesh in form of a scalable soft core array with a reconfigurable interconnect and implement it on FPGA technology in order to create a prototype platform. We present an overall hardware/software tool flow for generating and programming reconfigurable mesh prototypes. The new language ARMLang and a corresponding compiler facilitate the programming of the massively parallel processor arrays. To our knowledge, this work is the first practical study of word-level reconfigurable meshes. To analyze the performance of our implementation we study four algorithmic kernels from the application domains arithmetic, sorting, graph algorithms and imaging. For each kernel, we devise a reconfigurable mesh program in ARMLang, compile it to our soft core array and measure its runtime depending on the mesh size. Then, we compare the runtimes to two sequential implementations of the algorithms, which are executed on two single core systems. The results show that many-cores leveraging the reconfigurable mesh model can efficiently use a vast number of processing elements and that, for the chosen algorithms, they come close to optimally parallelized programs.

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“…Several constant time sorting algorithms for reconfigurable meshes were proposed which sort N numbers on meshes of size N Â N [8], [53], [54].…”

Section: Sorting and Selection: Schnorr And Shamirmentioning

confidence: 99%

An FPGA-Based Reconfigurable Mesh Many-Core

Giefers

Platzner

2014

IEEE Trans. Comput.

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“…Computing models for a p-sorter do exist. For example, it is known that p elements can be sorted in yI time on a reconfigurable mesh of size p Â p [13], [17], [19], [20]. A reconfigurable mesh is a multiprocessor system in which the processors are connected by a bus system whose configuration can be dynamically changed to suit computational needs.…”

Section: Introductionmentioning

confidence: 99%

How to sort N items using a sorting network of fixed I/O size

Olariu

Pinotti

Zheng

1999

IEEE Trans. Parallel Distrib. Syst.

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“…Refs. [1,4,11,15,16,26] Even in the most powerful CRCW PRAM, we know that sorting takes fl( lo ffi 0 " ) time given only a polynomial number of processors. Thus the reconfigurable network seems to a be an attractive model of computing.…”

Section: Introductionmentioning

confidence: 99%

“…For the same time bound, the processor bound has been reduced to n 2 by Refs. [1,4,11,15,16]. The later algorithm is the best possible under some weak assumptions.…”

Section: Introductionmentioning

confidence: 99%

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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Sorting n numbers on n*n reconfigurable meshes with buses

Cited by 48 publications

References 16 publications

An FPGA-Based Reconfigurable Mesh Many-Core

An FPGA-Based Reconfigurable Mesh Many-Core

How to sort N items using a sorting network of fixed I/O size

Permutation Routing and Sorting on the Reconfigurable Mesh

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