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Supporting the hypercube programming model on mesh architectures

Thomas M. Stricker
1992 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92  
A fast merge sorter based on the bitonic network serves as an example to show how a simple hypercube algorithm can outperform most of the asymptotically optimal mesh algorithms for practical machine sizes  ...  The bitonic merge sort, a simple hypercube algorithm, contains a fair amount of fine grain parallelism not found in standard mesh algorithms.  ...  Thanks also for the many helpful discussion with our theory community at CMU, particularly with Anja Feldmann, Gary Miller and Eric Schwabe.  ... 
doi:10.1145/140901.140917 dblp:conf/spaa/Stricker92 fatcat:ty7dwp7qgbeafoz5cmxtrabbim

Sorting and selection on interconnection networks [chapter]

Sanguthevar Rajasekaran
1995 DIMACS Series in Discrete Mathematics and Theoretical Computer Science  
In this paper we identify techniques that have been employed in the design of sorting and selection algorithms for various interconnection networks.  ...  For the sake of comparisons, we also list PRAM algorithms.  ...  The Mesh The first asymptotically optimal sorting algorithm for the mesh was given by Thompson and Kung [63] . Their algorithm can sort n numbers on a √ n× √ n Mesh in O( √ n) time.  ... 
doi:10.1090/dimacs/021/19 dblp:conf/dimacs/Rajasekaran94 fatcat:gw6blsftargqffge4p5nl3bgnm

Randomized Algorithms on the Mesh [chapter]

Lata Narayanan
1999 Combinatorial Optimization  
The mesh-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based on a mesh topology.  ...  In this paper, we survey the results on three fundamental problems in parallel computation: routing, sorting, and selection, and demonstrate that randomized algorithms for these problems on the mesh are  ...  In this paper, we discuss the fundamental problems of routing, sorting and selection on mesh-connected parallel computers.  ... 
doi:10.1007/978-1-4613-3282-4_4 fatcat:nrvuh22a5neldjgysyftydy3ne

Reconfigurable Architectures and Algorithms: A Research Survey

Rajeev Wankar, Rajendra Akerkar
2009 International Journal of Computer Science and Applications  
Following the years several new architectures and efficient algorithms for these were proposed, and their implementation using FPGA's have been shown.  ...  This paper presents a survey on the different architectures proposed, and few important algorithms presented for these specialized architectures over the period of last two decades.  ...  [CCCS90] , proposed an algorithm to perform semi-group computations in O(n 1/8 ) time having ( ) 8 / 5 8 / 5 N N × rectangular 2-mesh connected computers with multiple broadcasting.  ... 
dblp:journals/ijcsa/WankarA09 fatcat:4ge43cflzjfgrnd6uggrs7hb3u

Randomized algorithms on the mesh [chapter]

Lata Narayanan
1998 Lecture Notes in Computer Science  
The mesh-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based on a mesh topology.  ...  In this paper, we survey the results on three fundamental problems in parallel computation: routing, sorting, and selection, and demonstrate that randomized algorithms for these problems on the mesh are  ...  In this paper, we discuss the fundamental problems of routing, sorting and selection on mesh-connected parallel computers.  ... 
doi:10.1007/3-540-64359-1_715 fatcat:5l453vvbzjhrpoyytuwn45dcbu

Adaptive AT2 optimal algorithms on reconfigurable meshes

M Manzur Murshed, Richard P Brent
2000 Parallel Computing  
We support our idea by developing adaptive algorithms for sorting items and computing the contour of maximal elements of a set of planar points on RM. Ó (M.  ...  In this paper, we introduce, for the ®rst time, the idea of adaptive algorithm which runs on RM of variable sizes without compromising the AT 2 optimality.  ...  Dehne [3] gives an AT 2 optimal algorithm for solving m-contour problem on a mesh of size n p  n p in O n p time.  ... 
doi:10.1016/s0167-8191(00)00060-0 fatcat:m4lpsleckjehhnstyemhmuh42y

Page 1574 of Mathematical Reviews Vol. 55, Issue 5 [page]

1978 Mathematical Reviews  
Sorting on a mesh-connected parallel computer. Comm. ACM 20 (1977), no. 4, 263-271. Several sorting algorithms for ILLIAC-IV type machines are discussed.  ...  Optimal polyphase sorting. SIAM J. Comput. 6 (1977), no. 1, 1-39. A system of algorithms is presented which provide an asymp- totically optimal method for sorting a large volume of data.  ... 

An Optimal Time-Power Tradeoff for Sorting on a Mesh-Connected Computer with On-Chip Optics

Patrick Poon, Quentin F. Stout
2014 International Journal of Networking and Computing  
Furthermore, this layout is shown to be optimal in terms of the time-power tradeoff required for sorting.  ...  For sorting, standard mesh algorithms minimize time and total data movement, and hence constraining the mesh to use only half its processors at any instant must double the time.  ...  Our primary contribution is an optimal sorting algorithm, and proof of optimality, for a 2-dimensional mesh-connected computer augmented by optical interconnections.  ... 
doi:10.15803/ijnc.4.1_70 fatcat:qcddni7fynhlrmscaturoxrapq

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

S. Rajasekaran
1995 Journal of Algorithms  
All the above mentioned algorithms have optimal queue length, namely k+o(k). These algorithms also extend to higher dimensional meshes.  ...  All the above mentioned algorithms have optimal queue length, namely k + o(k). These algorithms also extend to higher dimensional meshes.  ...  Mesh Connected Computers The fixed connection machine assumed in this paper is the Mesh Connected Computer.  ... 
doi:10.1006/jagm.1995.1042 fatcat:khrgnkf22vcxlij2j4x45vw2dq

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

S. Rajasekaran
1996 IEEE transactions on computers  
We provide an improved algorithm for 1 − 1 routing and a matching sorting algorithm.  ...  Mesh connected computers have become attractive models of computing because of their varied special features.  ...  Acknowledgements I am thankful to Sunil Shende for introducing me to this area. I also would like to thank Viktor K. Prasanna and Assaf Schuster for providing me with a number of relevant articles.  ... 
doi:10.1109/12.509905 fatcat:ys5nysamy5a2haxawmfquk7geu

PERMUTATION ROUTING AND SORTING ON THE RECONFIGURABLE MESH

SANGUTHEVAR RAJASEKARAN, THEODORE MCKENDALL
1998 International Journal of Foundations of Computer Science  
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.  ...  A trivial lower bound for routing on M r will be n 2 . On the PARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal.  ...  Optimal algorithms have been discovered for packet routing and sorting on the conventional mesh.  ... 
doi:10.1142/s0129054198000143 fatcat:y3wwhwr4kbhorbuhzkobm236ty

Simple and Efficient Mesh Layout with Space-Filling Curves

Huy T. Vo, Claudio T. Silva, Luiz F. Scheidegger, Valerio Pascucci
2012 Journal of Graphics Tools  
Recently, Yoon et al. have shown that it is possible to construct an optimal cache-oblivious mesh layout (COML) for surface and volume data.  ...  We present a simple and efficient algorithm to compute cache-friendly layouts of unstructured geometric data.  ...  We would like to thank the Stanford University Computer Graphics Laboratory and XYZ RGB Inc. for the scanned models.  ... 
doi:10.1080/2151237x.2012.641828 fatcat:y67eqpmt4fgwhl6rukdvxlco7m

Page 1904 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
We provide an improved algorithm for 1-1 routing and a matching sorting algorithm.  ...  Summary: “Star connected cycles are shown to be undirected Cayley graphs, and the graph automorphism group is determined. A routing algorithm is given, which finds an optimal path in polynomial time.  ... 

Page 7280 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
We present an optimal O(n loga )-time (where o = \Z|) algorithm for the external inverse pattern matching problem. This substantially improves the O(nmloga)-time algorithm given by A. Amir, A.  ...  The authors then proceed to analyze existing and new dynamic algorithms for the problems of maximum car- dinality matching, minimum spanning forest, connectivity, 2-edge connectivity, k-edge connectivity  ... 

An Efficient Implementation of Batcher's Odd-Even Merge Algorithm and Its Application in Parallel Sorting Schemes

Kumar, Hirschberg
1983 IEEE transactions on computers  
The previous best sorting algorithm requires 14 n route steps for practical values of n, 4 < n < 512 (i.e., mesh-connected processor arrays containing 16 to 262 144 processors).  ...  The merge algorithms for the mesh-connected processor array use wrap around connections. These connections can be avoided at the expense of some extra hardware.  ...  Kung have made use of Batcher's odd-even merge algorithm to implement a sorting scheme for mesh-connected computers which requires -6n + 0(n2/3 log n) route steps and n + 0(n2/3 log n) compare-exchange  ... 
doi:10.1109/tc.1983.1676217 fatcat:mejvvttx2fhgxlflt65wacnwjq
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