- Article

Yang, X., Megson, G.M., Tang, Y.Y. and Xing, Y. 2008. Largest connected component of a star graph with faulty vertices. *International Journal of Computer Mathematics.* 85 (12), pp. 1771-1778.

Title | Largest connected component of a star graph with faulty vertices |
---|---|

Authors | Yang, X., Megson, G.M., Tang, Y.Y. and Xing, Y. |

Abstract | In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n≥3) with up to 2n-4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph. |

Journal | International Journal of Computer Mathematics |

Journal citation | 85 (12), pp. 1771-1778 |

ISSN | 0020-7160 |

Year | Dec 2008 |

Publisher | Taylor & Francis |

Digital Object Identifier (DOI) | doi:10.1080/00207160701619200 |

Publication dates | |

Published | Dec 2008 |

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A n-bit reconfigurable scalar quantiser

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Pipelining considerations for an FPGA case

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Final Report, EPSRC Grant, REFLEX

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A family of efficient regular arrays for band and sparse matrix inversion using Monte Carlo methods

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Quantitative evaluation of three reconfiguration strategies on FPGAs: a case study

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Accelerating JPEG compression with a dynamically reconfigurable FPGA systolic array

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Final Report, EPSRC Grant GR/L35089/01: systolic and regular array composition environment (SARACEN)

Megson, G.M. 2000. *Final Report, EPSRC Grant GR/L35089/01: systolic and regular array composition environment (SARACEN).* EPSRC.

Fault-tolerant ring embedding in a honeycomb torus with node failures

Megson, G.M., Liu, X. and Yang, X. 1999. Fault-tolerant ring embedding in a honeycomb torus with node failures. *Parallel Processing Letters.* 9 (4), pp. 551-561.

Honeycomb tori are Hamiltonian

Megson, G.M., Yang, X. and Liu, X. 1999. Honeycomb tori are Hamiltonian. *Information Processing Letters.* 72 (3-4), pp. 99-103.

Experiences using reconfigurable FPGAs in implementing Monte-Carlo methods

Plaks, T.P., Cadenas, O. and Megson, G.M. 1999. Experiences using reconfigurable FPGAs in implementing Monte-Carlo methods. in: Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA 1999, June 28 - Junlly 1, 1999, Las Vegas, Nevada, USA CSREA Press. pp. 1131-1137

Parallel algorithms for knapsack type problems

Aleksandrov, V.N. and Megson, G.M. 1999. *Parallel algorithms for knapsack type problems.* World Scientific Publishing.

Systolic arrays for the Haar transform

Megson, G.M. 1998. Systolic arrays for the Haar transform. *Computers and Digital techniques, IEE Proceedings E.* 145 (6), pp. 403-410.

Neural network analysis of hue spectra from natural images

Robertson, C. and Megson, G.M. 1998. Neural network analysis of hue spectra from natural images. in: Smith, G.D., Steele, N.C. and Albrecht, R.F. (ed.) Artificial neural nets and genetic algorithms: proceedings of the international conference in Norwich, U.K., 1997 Springer.

Static multiprocessor task graph scheduling in the genetic paradigm: a comparison of genotype representations, research report no. 98-25

Rebreyend, P., Sandnes, F.E. and Megson, G.M. 1998. *Static multiprocessor task graph scheduling in the genetic paradigm: a comparison of genotype representations, research report no. 98-25.* Lyon, France Ecole Normale Superieure de Lyon, Laboratoire de Informatique du Parallelisme.

Creation of reconfigurable hardware objects in PVM environments

Megson, G.M., Fish, R.S. and Clarke, D.N.J. 1998. Creation of reconfigurable hardware objects in PVM environments. in: Alexandrov, V.N. and Dongarra, J. (ed.) Recent advances in parallel virtual machine and message passing interface: 5th European PVM/MPI Users' Group Meeting Liverpool, UK, September 7–9, 1998: proceedings Berlin Springer.

Synthesis of a systolic array genetic algorithm

Megson, G.M. and Bland, I.M. 1998. Synthesis of a systolic array genetic algorithm. in: Proceedings of the first merged International Parallel Processing Symposium & Symposium on Parallel and Distributed Processing, March 30-April 3, 1998, Orlando, Florida Los Alamitos, USA IEEE . pp. 316-320

The systolic array genetic algorithm, an example of systolic arrays as a reconfigurable design methodology

Bland, I.M. and Megson, G.M. 1998. The systolic array genetic algorithm, an example of systolic arrays as a reconfigurable design methodology. in: Pocek, K.L. and Arnold, J.M. (ed.) IEEE symposium on FPGAs for custom computing machines, 1998 IEEE . pp. 260-261

Systolic array library for hardware genetic algorithms

Bland, I.M. and Megson, G.M. 1998. Systolic array library for hardware genetic algorithms. *MPCS 98.* Colorado Springs 6th-9th April 1998

Scalar quantisation using a fast systolic array

Megson, G.M. and Diemoz, E. 1997. Scalar quantisation using a fast systolic array. *Electronics Letters.* 33 (17), pp. 1435-1437.

Efficient operator pipelining in a bit serial genetic algorithm engine

Bland, I.M. and Megson, G.M. 1997. Efficient operator pipelining in a bit serial genetic algorithm engine. *Electronics Letters.* 33 (12), pp. 1026-1028.

Generic systolic array for genetic algorithms

Megson, G.M. and Bland, I.M. 1997. Generic systolic array for genetic algorithms. *Computers and Digital techniques, IEE Proceedings E.* 144 (2), pp. 107-119.

Improved static multiprocessor scheduling using cyclic task graphs: a genetic approach

Sandnes, F.E. and Megson, G.M. 1997. Improved static multiprocessor scheduling using cyclic task graphs: a genetic approach. *2nd Workshop on Randomized Parallel Computing - IPPS97.* Geneva, Switzerland 1 April 1997

Improved static multiprocessor scheduling using cyclic task graphs: a genetic approach

Sandnes, F.E. and Megson, G.M. 1997. Improved static multiprocessor scheduling using cyclic task graphs: a genetic approach. in: D'Hollander, E.H., Joubert, G.R., Peters, F.J. and Trottenburg, U. (ed.) Parallel Computing: Fundamentals, Applications and New Directions, Proceedings of the Conference ParCo'97, 19-22 September 1997, Bonn, Germany Elsevier.

Automatic parallelization for a class of regular computations

Megson, G.M. and Chen, X. 1997. *Automatic parallelization for a class of regular computations.* World Scientific Publishing.

Mapping a generic systolic array for genetic algorithms onto FPGAs: theory and practice

Megson, G.M. and Bland, I.M. 1997. Mapping a generic systolic array for genetic algorithms onto FPGAs: theory and practice. in: D'Hollander, E.H., Joubert, G.R., Peters, F.J. and Trottenburg, U. (ed.) Parallel Computing: Fundamentals, Applications and New Directions, Proceedings of the Conference ParCo'97, 19-22 September 1997, Bonn, Germany Elsevier.

Implementing a generic systolic array for genetic algorithms

Bland, I.M. and Megson, G.M. 1997. Implementing a generic systolic array for genetic algorithms. *First Online Workshop on Soft Computing, (WSC1).* Nagoya, Japan 19 - 31 Aug 1996 pp. 268-274

Systolic random number generation for genetic algorithms

Bland, I.M. and Megson, G.M. 1996. Systolic random number generation for genetic algorithms. *Electronics Letters.* 32 (12), pp. 1069-1070.

A hybrid genetic algorithm applied to automatic parallel controller code generation

Sandnes, F.E. and Megson, G.M. 1996. A hybrid genetic algorithm applied to automatic parallel controller code generation. in: Proceedings of the Eighth Euromicro Workshop on Real-Time Systems, 1996 IEEE . pp. 70-75

Genetic algorithms applied to automatic parallel controller code generation

Megson, G.M. and Sandnes, F.E. 1996. Genetic algorithms applied to automatic parallel controller code generation. *International Symposium on SOFT computing: SOCO 96.* University of Reading 26 - 28 Mar 1996

Automatic synthesis of parallel algorithms

Megson, G.M., Rapanotti, L. and Chen, X. 1996. Automatic synthesis of parallel algorithms. in: Ferreira, A. and Pardalos, P. (ed.) Solving Combinatorial Optimization Problems in Parallel: Berlin Springer.

Exploiting reconfigurability through high level synthesis

Megson, G.M. 1996. Exploiting reconfigurability through high level synthesis. in: IEE Colloquium on Hardware-Software Cosynthesis for Reconfigurable Systems (Digest No: 1996/036) London Institute of Electrical Engineers. pp. 5/1-5/4

Systolic algorithms in numerical analysis

Brudaru, O., Megson, G.M. and Galea, D. 1996. *Systolic algorithms in numerical analysis.* Bucharest Editura Academiei Romane.

Solving systems of linear algebraic equations by Monte Carlo method on regular arrays

Aleksandrov, V.N. and Megson, G.M. 1996. Solving systems of linear algebraic equations by Monte Carlo method on regular arrays. in: Vollmar, R., Jossifov, V. and Erhard, W. (ed.) Parcella '96: proceedings of the 7th international workshop on parallel processing by cellular automata and arrays held in Berlin, September 16-20 1996 Akademie Verlag.

Final Report, EPSRC Grant GR/H 46725: recurrence for-loop extensions (reflex)

Gurd, J.R. and Megson, G.M. 1996. *Final Report, EPSRC Grant GR/H 46725: recurrence for-loop extensions (reflex).* EPSRC.

A general methodology of partitioning and mapping for given regular arrays

Chen, X. and Megson, G.M. 1995. A general methodology of partitioning and mapping for given regular arrays. *IEEE Transactions on Parallel and Distributed Systems.* 6 (10), pp. 1100-1107.

Uniformization techniques for reducible integral recurrence equations

Rapanotti, L. and Megson, G.M. 1995. Uniformization techniques for reducible integral recurrence equations. in: Moonen, M.S. and Catthoor, F. (ed.) Algorithms and parallel VLSI architectures III: proceedings of the international workshop, algorithms and parallel VLSI Architectures III, Leuven, Belgium, August 29-31, 1994 Elsevier. pp. 283-294

Regularising transformations for integral dependencies

Megson, G.M. and Rapanotti, L. 1995. Regularising transformations for integral dependencies. in: Ferreira, A. and Rolim, J. (ed.) Parallel algorithms for irregular problems: state of the art Springer. pp. 297-322

Determining n-D convex hulls using parallel facial lattice exploration

Megson, G.M. and Eyoh, E.O. 1995. Determining n-D convex hulls using parallel facial lattice exploration. *ParCo'95: Fifth International Conference on Parallel Computing.* Ghent, Belgium 19 - 22 Sep 1995

A synthesis method of LSGP partitioning for given-shape regular arrays

Megson, G.M. and Chen, X. 1995. A synthesis method of LSGP partitioning for given-shape regular arrays. in: Proceedings of the 9th International Parallel Processing Symposium, April 25-28, 1995, Santa Barbara, California Los Alamitos, USA IEEE . pp. 234-238

Software tools for algorithmic engineering

Megson, G.M. 1994. Software tools for algorithmic engineering. *Innovation.* 25, p. 15.

Systolic state estimators for discrete-time controllers

Megson, G.M. 1994. Systolic state estimators for discrete-time controllers. *Electronics Letters.* 30 (11), pp. 914-915.

Systolic algorithm design environments (SADEs)

Megson, G.M. and Comish, D. 1994. Systolic algorithm design environments (SADEs). in: Megson, G.M. (ed.) Transformational approaches to systolic design London Chapman & Hall. pp. 205-239

Automatic derivation of systolic algorithms for Kalman filtering

Megson, G.M. and Comish, D. 1994. Automatic derivation of systolic algorithms for Kalman filtering. in: McWhirter, J.G. (ed.) Mathematics in signal processing III: based on the proceedings of the third conference organized by the Institute of Mathematics and Its Applications on mathematics in signal processing, held at the University of Warwick in December 1992 Clarendon Press.

Partitioning and mapping for lower dimensional given arrays

Megson, G.M. and Chen, X. 1994. Partitioning and mapping for lower dimensional given arrays. in: Second Euromicro Workshop on Parallel and Distributed Processing, University of Malaga, Spain, January 26-28, 1994: proceedings Los Alamitos, USA IEEE . pp. 149-155

Fixed sized systolic arrays for matrix inversion using a Monte Carlo method

Megson, G.M., Aleksandrov, V.N. and Dimov, I.T. 1994. Fixed sized systolic arrays for matrix inversion using a Monte Carlo method. in: Dimov, I.T., Sendov, B.L. and Vassilevski, P.S. (ed.) Advances in numerical methods and applications: proceedings of the 3rd international conference World Scientific Publishing. pp. 255-265

Systolic matrix inversion using a Monte Carlo method

Megson, G.M., Aleksandrov, V.N. and Dimov, I.T. 1994. Systolic matrix inversion using a Monte Carlo method. *International Journal of Parallel, Emergent and Distributed Systems.* 3 (3 & 4), pp. 311-330.

Systolic matrix inversion by Monte Carlo method

Megson, G.M., Aleksandrov, V.N. and Dimov, I.T. 1994. Systolic matrix inversion by Monte Carlo method. in: Ames, W.F. (ed.) Proceedings of the 14th IMACS World Congress on Computation and Applied Mathematics [also] IMACS '94, July 11-15, 1994, Georgia Institute of Technology, Atlanta, Georgia, USA Georgia Institute of Technology. pp. 1371-1373

Towards a formal model of algorithmic engineering

Megson, G.M. 1994. Towards a formal model of algorithmic engineering. in: Dimov, I.T. and Tonev, O. (ed.) Advances in parallel algorithms IOS Press. pp. 184-193

Final Report, SERC Grant GR/F 80494: design of multi-layer systolic algorithms

Megson, G.M. 1994. *Final Report, SERC Grant GR/F 80494: design of multi-layer systolic algorithms.* Science and Engineering Research Council.

CAD tools for the automatic synthesis of parallel algorithms in control

Megson, G.M. 1994. CAD tools for the automatic synthesis of parallel algorithms in control. in: International Conference on Control '94: 21-24 March 1994: venue, University of Warwick, Coventry, UK London Institution of Electrical Engineers.

Implementation and evaluation of parallel n-D convex hull algorithms

Eyoh, E.O. and Megson, G.M. 1994. Implementation and evaluation of parallel n-D convex hull algorithms. in: Joubert, G.R., Trystram, D., Peters, F.J. and Evans, D.J. (ed.) Parallel computing: trends and applications: proceedings of the international conference ParCo93, Grenoble, France 7-10 September, 1993 Amsterdam ; London Elsevier.

A space-time modeler for systlic algorithms

Diemoz, E. and Megson, G.M. 1994. A space-time modeler for systlic algorithms. *Advances in Engineering Software.* 20 (1), pp. 29-41.

Systolic designs for evaluating linear combinations of Chebyshev polynomials

Brudaru, O. and Megson, G.M. 1994. Systolic designs for evaluating linear combinations of Chebyshev polynomials. in: Halatsis, C., Maritsas, D., Philokyprou, G. and Theodoridis, S. (ed.) PARLE'94 Parallel Architectures and Languages Europe: 6th International PARLE Conference Athens, Greece, July 4–8, 1994: proceedings Berlin Springer.

Systolic arrays for accelerating iteration processes

Brudaru, O. and Megson, G.M. 1994. Systolic arrays for accelerating iteration processes. in: Jesshope, C.R., Jossifov, V. and Wilhelmi, W. (ed.) Parcella '94: proceedings of the 6th international workshop on parallel processing by cellular automata and arrays held in Potsdam, September 21-23 1994 Berlin Akademie Verlag.

Mapping knapsack type problems on 2D regular arrays: two case studies

Aleksandrov, V.N., Megson, G.M. and Fidanova, S. 1994. Mapping knapsack type problems on 2D regular arrays: two case studies. in: Jesshope, C.R., Jossifov, V. and Wilhelmi, W. (ed.) Parcella '94: proceedings of the 6th international workshop on parallel processing by cellular automata and arrays held in Potsdam, September 21-23 1994 Berlin Akademie Verlag.

Systolic partitioning algorithms

Megson, G.M. 1993. Systolic partitioning algorithms. *Information Processing Letters.* 46 (1), pp. 13-18.

Efficient systolic Broyden algorithm

Megson, G.M. 1993. Efficient systolic Broyden algorithm. *Electronics Letters.* 29 (1), p. 93.

The givens-batcher reduction algorithm and matrix triangularisation

Megson, G.M. 1993. The givens-batcher reduction algorithm and matrix triangularisation. *International Journal of Computer Mathematics.* 47 (3&4), pp. 199-208.

The derivation of uniform recurrence equations using the knapsack problem

Megson, G.M. 1993. The derivation of uniform recurrence equations using the knapsack problem. *International Journal of Parallel, Emergent and Distributed Systems.* 1 (2), pp. 127-140.

Multi-layer systolic algorithms

Megson, G.M. 1993. Multi-layer systolic algorithms. *DTI/SERC JFIT Technical Conference.* Keele 23 - 24 Mar 1993

Mapping a class of run-time dependencies onto regular arrays

Megson, G.M. 1993. Mapping a class of run-time dependencies onto regular arrays. in: Proceedings of Seventh International Parallel Processing Symposium Los Alamitos, USA IEEE . pp. 97-104

Pre-processing stage in solving ODEs with extrapolation methods

Brudaru, O. and Megson, G.M. 1993. Pre-processing stage in solving ODEs with extrapolation methods. *Studia Universitatis Babes-Bolyai, Thematica.* XXXVII (3), pp. 31-57.

A fast Faddeev array

Megson, G.M. 1992. A fast Faddeev array. *IEEE Transactions on Computers.* 41 (12), pp. 1594-1600.

Keeping a finger on the pulse

Megson, G.M. 1992. Keeping a finger on the pulse. *Parallelogram International: international journal of high performance computing.*

Systolic designs for Aitken's root finding method

Megson, G.M., Brudaru, O. and Comish, D. 1992. Systolic designs for Aitken's root finding method. *Parallel Computing.* 18 (4), pp. 415-429.

More on systolic line drawing

Megson, G.M. and Evans, D.J. 1992. More on systolic line drawing. *Parallel Computing.* 18 (2), pp. 355-358.

VLSI systolic arrays for table based algorithms

Megson, G.M. and Evans, D.J. 1992. VLSI systolic arrays for table based algorithms. in: Evans, D.J. (ed.) Advances in parallel computing: a research annual JAI Press.

An introduction to systolic algorithm design

Megson, G.M. 1992. *An introduction to systolic algorithm design.* Oxford Clarendon.

Practical steps towards algorithmic engineering

Megson, G.M. 1992. Practical steps towards algorithmic engineering. in: IEE Colloquium on applications of parallel and distributed processing in automation and control on Friday, 13 November 1992 Institution of Electrical Engineers.

Experimenting with DTAGS: an interactive synthesis package

Megson, G.M. 1992. Experimenting with DTAGS: an interactive synthesis package. in: Colloquium on Generic Parallelisation of Algorithms for Control and Simulation Institution of Electrical Engineers.

Two-dimensional systolic array for the column-by-column QD algorithm

Brudaru, O. and Megson, G.M. 1991. Two-dimensional systolic array for the column-by-column QD algorithm. *Computers and Digital techniques, IEE Proceedings E.* 138 (6), pp. 401-406.

A systolic simplex algorithm

Evans, D.J. and Megson, G.M. 1991. A systolic simplex algorithm. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 417-445

Compact systolic arrays for incomplete matrix factorisation methods

Evans, D.J. and Megson, G.M. 1991. Compact systolic arrays for incomplete matrix factorisation methods. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 321-373

Matrix inversion by systolic rank annihilation

Evans, D.J. and Megson, G.M. 1991. Matrix inversion by systolic rank annihilation. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 159-197

Systolic arrays for group explicit methods for solving first order hyperbolic equations

Megson, G.M. and Evans, D.J. 1991. Systolic arrays for group explicit methods for solving first order hyperbolic equations. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 215-231

Construction of extrapolation tables by systolic arrays for solving ordinary differential equations

Evans, D.J. and Megson, G.M. 1991. Construction of extrapolation tables by systolic arrays for solving ordinary differential equations. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 199-213

Romberg integration using systolic arrays

Evans, D.J. and Megson, G.M. 1991. Romberg integration using systolic arrays. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 183-197

On systolic arrays for complex matrix problems

Megson, G.M. and Evans, D.J. 1991. On systolic arrays for complex matrix problems. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 153-165

Algorithmic fault tolerance for matrix operations on triangular arrays

Megson, G.M. and Evans, D.J. 1991. Algorithmic fault tolerance for matrix operations on triangular arrays. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 139-151

Triangular systolic arrays for matrix product and factorisation

Megson, G.M. and Evans, D.J. 1991. Triangular systolic arrays for matrix product and factorisation. in: Evans, D.J. (ed.) Systolic Algorithms Philadelphia, USA Gordon and Breach Science Publishers. pp. 115-137

Systolic algorithm design environments

Megson, G.M. and Comish, D. 1991. Systolic algorithm design environments. in: Second International Specialist Seminar on the Design and Application of Parallel Digital Processors, 15-19 April, 1991, venue The Gulbenkian Foundation, Lisbon, Portugal London Institution of Electrical Engineers. pp. 100-104

A systolic Broyden algorithm

Megson, G.M. 1991. A systolic Broyden algorithm. in: Second International Specialist Seminar on the Design and Application of Parallel Digital Processors, 15-19 April, 1991, venue The Gulbenkian Foundation, Lisbon, Portugal London Institution of Electrical Engineers. pp. 127-131

Unifying structures for parallel algorithms in control

Megson, G.M. 1991. Unifying structures for parallel algorithms in control. *First European Control Conference.* Grenoble Alpes Congrès Centre, Grenoble, France 02 - 05 Jul 1991

Systolic rank updating and the solution of non-linear equations

Megson, G.M. 1991. Systolic rank updating and the solution of non-linear equations. in: Fifth International Parallel Processing Symposium: proceedings IEEE . pp. 344-351

Systolic algorithms for B-spline patch generation

Megson, G.M. 1991. Systolic algorithms for B-spline patch generation. *Journal of Parallel and Distributed Computing.* 11 (3), pp. 231-238.

Fast multi-layer systolic arrays for Kalman filtering

Megson, G.M. 1991. Fast multi-layer systolic arrays for Kalman filtering. in: Deprettere, F. and Van der Veen, A.J. (ed.) Algorithms and parallel VLSI architectures. Volume B, Proceedings Elsevier.

Book review: Vector models for data-parallel computing

Megson, G.M. 1991. Book review: Vector models for data-parallel computing. *Journal of Computer Systems Science & Engineering.*

Book review: Parallel computing 89

Megson, G.M. 1991. Book review: Parallel computing 89. *Journal of Computer Systems Science & Engineering.*

Book review: Computing with Parallel Architectures – T. Node, ISBN 0792312252, Kluwer Academic Publishers Groups

Megson, G.M. 1991. Book review: Computing with Parallel Architectures – T. Node, ISBN 0792312252, Kluwer Academic Publishers Groups. *Computer Journal.* 34 (6), p. 573.

Automatic systolic algorithm design II: a practical approach

Megson, G.M. 1991. Automatic systolic algorithm design II: a practical approach. *ICL Parallel Computing.* University of Newcastle upon Tyne pp. 19-36

Automatic systolic algorithm design I: basic synthesis techniques

Megson, G.M. 1991. Automatic systolic algorithm design I: basic synthesis techniques. *ICL Parallel Computing.* University of Newcastle upon Tyne

A systolic simplex algorithm

Evans, D.J. and Megson, G.M. 1991. A systolic simplex algorithm. *International Journal of Computer Mathematics.* 38 (1&2), pp. 1-30.

An orthogonal systolic design for the assignment problem

Megson, G.M. and Evans, D.J. 1990. An orthogonal systolic design for the assignment problem. *Parallel Computing.* 16 (2-3), pp. 253-267.

Systolic arrays for group explicit methods for solving first order hyperbolic equations

Megson, G.M. and Evans, D.J. 1990. Systolic arrays for group explicit methods for solving first order hyperbolic equations. *Parallel Computing.* 16 (2-3), pp. 191-205.

Efficient systolic string matching

Megson, G.M. 1990. Efficient systolic string matching. *Electronics Letters.* 26 (24), pp. 2040-2042.

Improved matrix triangularisation using a double pipeline systolic array

Megson, G.M. and Gaston, F.M.F. 1990. Improved matrix triangularisation using a double pipeline systolic array. *Information Processing Letters.* 36 (2), pp. 103-109.

Sorting without exchanges on a bit-serial systolic array

Megson, G.M. 1990. Sorting without exchanges on a bit-serial systolic array. *Circuits, Devices and Systems, IEE Proceedings G.* 137 (5), pp. 345-352.

Transputer implementation of systolic arrays for model reduction

Megson, G.M. 1990. Transputer implementation of systolic arrays for model reduction. *Computers and Digital techniques, IEE Proceedings E.* 137 (5), pp. 343-352.

The systolic control ring instruction processor (SCRIP)

Megson, G.M. and Evans, D.J. 1990. The systolic control ring instruction processor (SCRIP). *Integration: the VLSI Journal.* 9 (3), pp. 287-302.

Transputer arrays and computer-aided control system design

Megson, G.M. 1990. Transputer arrays and computer-aided control system design. *Control Theory and Applications, IEE Proceedings D.* 137 (4), pp. 197-210.

Complex eigenproblem solution by a parallel norm-reducing Jacobi method

Megson, G.M. 1990. Complex eigenproblem solution by a parallel norm-reducing Jacobi method. *Journal of Computer Systems Science and Engineering.* 5 (3), pp. 159-168.

A systolic helix for matrix triangularisation with partial pivoting

Megson, G.M. 1990. A systolic helix for matrix triangularisation with partial pivoting. *Parallel Computing.* 14 (2), pp. 199-206.

The Givens Batcher Reduction (GBR) algorithm

Megson, G.M. 1990. The Givens Batcher Reduction (GBR) algorithm. *International Workshop on Algorithms and Parallel VLSI Architectures.* Pont-a-Mousson, France 10 - 16 Jun 1990

Ray tracing using the SCRIP machine

Popovic, R. and Megson, G.M. 1990. Ray tracing using the SCRIP machine. in: Evans, D.J., Joubert, G.R. and Peters, F.J. (ed.) Parallel computing 89: proceedings of the international conference, Leiden, 29 August-1 September 1989 Elsevier. pp. 387-396

A systolic array solution for the assignment problem

Megson, G.M. and Evans, D.J. 1990. A systolic array solution for the assignment problem. *The Computer Journal.* 33 (6), pp. 562-569.

An efficient double pipe systolic array for matrix product

Megson, G.M. and Evans, D.J. 1990. An efficient double pipe systolic array for matrix product. *The Computer Journal.* 33 (3), pp. 261-265.

On the suitability of higher block matrix forms for systolic LU decomposition

Megson, G.M. and Evans, D.J. 1990. On the suitability of higher block matrix forms for systolic LU decomposition. *Journal of New Generation Computer Systems.* 3 (2), pp. 143-158.

A systolic topelitz linear solver

Evans, D.J. and Megson, G.M. 1990. A systolic topelitz linear solver. in: McWhirter, J.G. (ed.) Mathematics in signal processing II: based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on mathematics in signal processing held at the University of Warwick in December 1988 Clarendon Press.

Rank annihilation on a ring of processors

Megson, G.M. 1990. Rank annihilation on a ring of processors. *Parallel Computing.* 13 (1), pp. 85-94.

Fast triangularization of a symmetric tridiagonal matrix

Evans, D.J. and Megson, G.M. 1989. Fast triangularization of a symmetric tridiagonal matrix. *Journal of Parallel and Distributed Computing.* 6 (3), pp. 663-678.

Algorithmic fault tolerance for matrix operations on triangular arrays

Megson, G.M. and Evans, D.J. 1989. Algorithmic fault tolerance for matrix operations on triangular arrays. *Parallel Computing.* 10 (2), pp. 207-219.

Systolic preconditioning algorithms for the iterative solution of sparse linear systems

Megson, G.M. and Evans, D.J. 1989. Systolic preconditioning algorithms for the iterative solution of sparse linear systems. *Journal of New Generation Computer Systems.* 2, pp. 111-128.

On systolic arrays for complex matrix problems

Megson, G.M. and Evans, D.J. 1989. On systolic arrays for complex matrix problems. *International Journal of Computer Mathematics.* 30 (1&2), pp. 103-116.

A systolic matrix norm generator

Evans, D.J. and Megson, G.M. 1989. A systolic matrix norm generator. in: Jesshope, C.R. (ed.) Major advances in parallel processing: seminar: papers and summaries Temple University. pp. 320-327

Systolic preconditioning algorithms for the jacobi iterative solution of sparse linear systems

Evans, D.J. and Megson, G.M. 1989. Systolic preconditioning algorithms for the jacobi iterative solution of sparse linear systems. in: Wolf, G., Legendi, T. and Schendel, U. (ed.) Parcella '88: 4th International workshop on parallel processing by cellular automata and arrays: Berlin, GDR, October 17–21, 1988: proceedings Berlin Springer.

Parallel and systolic algorithms for robot control

Evans, D.J. and Megson, G.M. 1989. Parallel and systolic algorithms for robot control. *IMA Conference of Robotics: Applied Mathematics and Computational Apsects.* Loughborough 12-14 July 1989

Hopscotch schemes for the solution of parabolic equations on area efficient systolic arrays

Evans, D.J. and Megson, G.M. 1989. Hopscotch schemes for the solution of parabolic equations on area efficient systolic arrays. in: McCanny, J., McWhirter, J.G. and Swartzlander, E. (ed.) Systolic array processors: 3rd International conference on systolic arrays: papers New York ; London Prentice Hall. pp. 62-72

Matrix power generation using an optical reduced-bandwidth systolic array

Megson, G.M. and Evans, D.J. 1988. Matrix power generation using an optical reduced-bandwidth systolic array. *Optoelectronics, IEE Proceedings J.* 135 (6), pp. 435-442.

Final report short-term transputer loan TR1/083

Megson, G.M. and O'Young, S.D. 1988. *Final report short-term transputer loan TR1/083.* Science and Engineering Research Council.

The unification of systolic differencing algorithms

Megson, G.M. and Evans, D.J. 1988. The unification of systolic differencing algorithms. *The Computer Journal.* 31 (1), pp. 83-91.

Triangular systolic arrays for matrix product and factorisation

Megson, G.M. and Evans, D.J. 1988. Triangular systolic arrays for matrix product and factorisation. *International Journal of Computer Mathematics.* 25 (3&4), pp. 321-343.

Short notes: improved matrix product computation using double-pipeline systolic arrays

Megson, G.M. and Evans, D.J. 1988. Short notes: improved matrix product computation using double-pipeline systolic arrays. *The Computer Journal.* 31 (6), pp. 567-569.

Improved matrix product computation using double-pipeline systolic arrays

Megson, G.M. and Evans, D.J. 1988. Improved matrix product computation using double-pipeline systolic arrays. *The Computer Journal.* 31 (6), pp. 567-569.

Compact systolic arrays for incomplete matrix factorisation methods

Megson, G.M. and Evans, D.J. 1988. Compact systolic arrays for incomplete matrix factorisation methods. *International Journal of Computer Mathematics.* 25 (3&4), pp. 235-286.

Transputer implementation of systolic arrays for model reduction

Megson, G.M. 1988. Transputer implementation of systolic arrays for model reduction. in: IEE Colloquium on Recent Advances in Parallel Processing for Control London Institution of Electrical Engineers. pp. 5/1-5/10

Implementing SVD computation for feedback control systems on transputer arrays

Megson, G.M. 1988. Implementing SVD computation for feedback control systems on transputer arrays. *CONPAR 88.* UMIST, Manchester 12 - 16 Sep 1988

Hardware accelerators for STABLE-H

Megson, G.M. 1988. Hardware accelerators for STABLE-H. in: International Conference on Control 88, 13-15 April 1988 London Institution of Electrical Engineers. pp. 104-109

The alternating group explict (AGE) systolic array for the solution of large linear systems

Evans, D.J. and Megson, G.M. 1988. The alternating group explict (AGE) systolic array for the solution of large linear systems. *IFIP Workshop on Parallel Processing.* Pisa, Italy 25-27 April 1988 pp. 241-260

Systolic arrays for group explicit methods for solving parabolic partial differential equations

Evans, D.J. and Megson, G.M. 1988. Systolic arrays for group explicit methods for solving parabolic partial differential equations. in: Bromley, K., Kung, S.Y. and Swartzlander, E. (ed.) Proceedings of the International Conference on Systolic Arrays, San Diego, California, 25-27 May 1988 Washington, D.C. The Computer Society. pp. 315-329

Systolic array for the quotient difference algorithm

Evans, D.J. and Megson, G.M. 1988. Systolic array for the quotient difference algorithm. *Computers and Digital techniques, IEE Proceedings E.* 135 (1), pp. 60-66.

Construction of extrapolation tables by systolic arrays for solving ordinary differential equations

Evans, D.J. and Megson, G.M. 1987. Construction of extrapolation tables by systolic arrays for solving ordinary differential equations. *Parallel Computing.* 4 (1), pp. 33-48.

Novel algorithms for the soft-systolic paradigm

Megson, G.M. 1987. *Novel algorithms for the soft-systolic paradigm.* PhD thesis Loughborough University of Technology Department of Computer Studies

The solution of parabolic differential equations by systolic marching techniques

Evans, D.J. and Megson, G.M. 1987. The solution of parabolic differential equations by systolic marching techniques. in: Vichnevetsky, R. and Stepleman, R.S. (ed.) Advances in computer methods for partial differential equations-VI: proceedings of the sixth IMACS International Symposium on Computer Methods for Partial Differential Equations, held at Lehigh University, Bethlehem, Pennsylvania, U.S.A., June 23-25, 1987 Liége, Belgium International Association for Mathematics and Computers in Simulation. pp. 44-52

Matrix inversion by systolic rank annihilation

Evans, D.J. and Megson, G.M. 1987. Matrix inversion by systolic rank annihilation. *International Journal of Computer Mathematics.* 21 (3), pp. 319-357.

Romberg integration using systolic arrays

Evans, D.J. and Megson, G.M. 1986. Romberg integration using systolic arrays. *Parallel Computing.* 3 (4), pp. 289-304.

Soft-systolic pipelined matrix algorithms

Megson, G.M. and Evans, D.J. 1986. Soft-systolic pipelined matrix algorithms. in: Feilmeier, M., Joubert, G.R. and Schendel, U. (ed.) Parallel computing 85: proceedings of the Second International Conference on Parallel Computing, held at the Freie Universität Berlin, 23-25, September 1985 Elsevier. pp. 171-180

LISA: a parallel processing architecture

Megson, G.M. and Evans, D.J. 1986. LISA: a parallel processing architecture. in: Händler, W., Haupt, D., Jeltsch, R., Juling, W. and Lange, O. (ed.) CONPAR 86: Conference on Algorithms and Hardware for Parallel Processing Aachen, September 17–19, 1986: proceedings Berlin ; New York Springer.

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