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An Efficient Algorithm for Gray-to-Binary Permutation on Hypercubes

C.T. Ho, M.T. Raghunath, S.L. Johnsson
1994 Journal of Parallel and Distributed Computing  
We give a nearly optimal algorithm for permuting data from a Gray code mapping to a binary code mapping on a hypercube with communication restricted to one input and one output channel per node at a time  ...  Both Gray code and binary code are frequently used in mapping arrays into hypercube architectures.  ...  Acknowledgments The authors wish to acknowledge that an algorithm similar to our Algorithm GB2 has independently been proposed by Steve Heller of Thinking Machines Corp.  ... 
doi:10.1006/jpdc.1994.1012 fatcat:flspr5cz65eq3baqq2bo6nev7m

Transposition of banded matrices in hypercubes: A nearly isotropic task

Emmanouel A. Varvarigos, Dimitri P. Bertsekas
1995 Parallel Computing  
We also derive a lower bound on the minimum number of steps required to transpose a banded matrix, which holds for any possible assignment of matrix columns to hypercube processors.  ...  Under this assignment, we give an algorithm to transpose the matrix in 2A steps. We prove that the algorithm given is optimal over all affine assignments of columns to processors.  ...  The Transposition Algorithm In this subsection we give an algorithm to transpose a banded matrix stored in a hypercube according to the Binary-Gray assignment.  ... 
doi:10.1016/0167-8191(94)00031-5 fatcat:4embubgvojaanjdv6j7zsnbl2q

Embedding cube-connected cycles graphs into faulty hypercubes

J. Bruck, R. Cypher, D. Soroker
1994 IEEE transactions on computers  
We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with  ...  Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults.  ...  ACKNOWLEDGMENT We would like to thank the anonymous referees for their helpful comments and suggestions.  ... 
doi:10.1109/12.324546 fatcat:nc6fz5qitjhbpcnbbmwo5hncvq

Efficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes

Zhiyong Liu, D.W. Cheung
1997 Computers and Mathematics with Applications  
A parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes is presented.  ...  Using n processors, the presented algorithm can finish LU decomposition of an n x n matrix in 0(n2/3 + O(n~/'~log 2 n)) steps, including computations as well as communications, and its efficiency is 1  ...  More importantly, when a mesh is embedded onto hypercube, for example, using the Gray code embedding, one may not be able to implement the systolic algorithm for matrix multiplication on an SIMD hypercube  ... 
doi:10.1016/s0898-1221(97)00052-7 fatcat:apchffmcujanha7wzunsds4sje

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  ...  This paper presents a method for mapping binary hypercube-algorithms onto lower dimensional meshes and analyzes this method in a model derived from the architecture of modern mesh machines.  ...  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

p-Adic scaled space filling curve indices for high dimensional data [article]

Patrick Erik Bradley, Markus Wilhelm Jahn
2019 arXiv   pre-print
This article generalises this concept to the systematic construction of p-adic versions of Hilbert curves based on affine transformations of the p-adic Gray code, and develops an efficient scaled indexing  ...  method for data taken from high-dimensional spaces based on these new curves, which with increasing dimension is shown to be less space consuming than the optimal standard static Hilbert curve index.  ...  Acknowledgement Norbert Paul is thanked for fruitful discussions.  ... 
arXiv:1904.07700v1 fatcat:rudsntrvr5h5pj63k5x3z5eekq

Solving elliptic partial differential equations on the hypercube multiprocessor

Tony F. Chan, Youcef Saad, Martin H. Schultz
1987 Applied Numerical Mathematics  
The binaryv reflected Gray code plays an important role for both the multigrid and the AD! algorithms.  ...  We-ie ~ the implementation of several classical methods for solving elliptic partial differential equations on the hypercube multiprocessor.  ...  A simple way of implementing ADI on the hypercube is to map a ring onto the hypercube and then perform an algorithm that is tailored for the ring.  ... 
doi:10.1016/0168-9274(87)90007-9 fatcat:2q2dxatnqjc3ffkpjynh3er7cq

Optimal all-to-all personalized exchange in self-routable multistage networks

Y. Yang, J. Wang
2000 IEEE Transactions on Parallel and Distributed Systems  
The newly proposed algorithm has yn time complexity for an n n network, which is optimal for all-to-all personalized exchange.  ...  Previous all-to-all personalized exchange algorithms were mainly developed for hypercube and mesh/torus networks.  ...  ACKNOWLEDGMENTS We would like to thank the anonymous referees of this article for their thoughtful and constructive comments.  ... 
doi:10.1109/71.841742 fatcat:3boeh55hu5ckzpqyyeftzbk5yi

Ordered fast fourier transforms on a massively parallel hypercube multiprocessor

Charles Tong, Paul N. Swarztrauber
1991 Journal of Parallel and Distributed Computing  
We examine design alternatives for ordered FFT algorithms on massively parallel hypercube multiprocessors such as the Connection Machine.  ...  A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine. interests are parallel numerical solution of partial differential equations, parallel algorithms for numerical  ...  Definition 2 : An index-digit permuted sequence to processor map is one in which the indices i j are permuted.  ... 
doi:10.1016/0743-7315(91)90028-8 fatcat:vf3icvow4vgalkfha3co35wb3e

Properties of Gray and Binary Representations

Jonathan Rowe, Darrell Whitley, Laura Barbulescu, Jean-Paul Watson
2004 Evolutionary Computation  
There are in fact many different Gray codes. Shifting is defined as a mechanism for dynamically switching from one Gray code representation to another in order to escape local optima.  ...  Gray codes are widely used in conjunction with genetic algorithms and bit-climbing algorithms for parameter optimization problems.  ...  Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation.  ... 
doi:10.1162/evco.2004.12.1.47 pmid:15096305 fatcat:oji3rcpkx5azbkra3nvaahw7be

Properties of Gray and Binary Representations

Jonathan Rowe, Darrell Whitley, Laura Barbulescu, Jean-Paul Watson
2004 Evolutionary Computation  
There are in fact many different Gray codes. Shifting is defined as a mechanism for dynamically switching from one Gray code representation to another in order to escape local optima.  ...  Gray codes are widely used in conjunction with genetic algorithms and bit-climbing algorithms for parameter optimization problems.  ...  Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation.  ... 
doi:10.1162/106365604773644323 pmid:15096305 fatcat:677myzv6x5f3jmqeqdx5d7r4ty

A fast algorithm to generate Beckett-Gray codes

Joe Sawada, Dennis Chi-Him Wong
2007 Electronic Notes in Discrete Mathematics  
We provide several heuristics to improve the efficiency of exhaustively generating Gray codes on length n binary strings.  ...  We then apply the heuristics to a restricted class of Gray codes on binary strings known as Beckett-Gray codes.  ...  There is an improvement by a factor of over 60 on the runtime for an exhaustive search for n = 6 when compared to [CNS07] , and over 9500 new Beckett-Gray codes for n = 7 were also discovered by our algorithm  ... 
doi:10.1016/j.endm.2007.07.091 fatcat:y7wpp6fjvna67o5h4rzyn65x7i

Finding Lean Induced Cycles in Binary Hypercubes [chapter]

Yury Chebiryak, Thomas Wahl, Daniel Kroening, Leopold Haller
2009 Lecture Notes in Computer Science  
In this paper, we propose an approach to finding a special class of induced cycles we call lean, based on an efficient propositional SAT encoding.  ...  The state of the art for computing such cycles relies on genetic algorithms, which are, however, unable to perform a complete search.  ...  They also thank the anonymous reviewers for suggestions on how to improve the draft.  ... 
doi:10.1007/978-3-642-02777-2_4 fatcat:uqhhxwrwpnctpn73rj5e6q6spi

Optimal and suboptimal processor allocation for hypercycle-based multiprocessors

N.J. Dimopoulos, V.V. Dimakopoulos
1995 IEEE Transactions on Parallel and Distributed Systems  
J 1 1J1 based on permutations of the hypercycle base, for both the optimal Hypercycle 43 Binary 3-cube r; 222 and the nonstatically optimal strategies.  ...  (Fig. 4 o more gray c es permIts t e recogmtlon O more su u s an thus increases the efficiency of the allocation. In the general case of hypercycles, the use of gray codes is not A.  ... 
doi:10.1109/71.342130 fatcat:d7gypmtfsvesll5pkmxw2v73hq

A scaled space-filling curve index applied to tropical rain forest tree distributions [article]

Markus Wilhelm Jahn, Patrick Erik Bradley
2019 arXiv   pre-print
In order to be able to process the increasing amount of spatial data, efficient methods for their handling need to be developed. One major challenge for big spatial data is access.  ...  The relative efficiency of the scaled Gray-Hilbert curve in comparison with the best static version is seen to depend on the distribution of the point cloud.  ...  They would also like to express their thanks to the Center for Tropical Forest Science of the Smithsonian Tropical Research Institute for providing the data set.  ... 
arXiv:1904.08053v2 fatcat:kz554te5vzg5pel6hvjad4nagy
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