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THE DIAMETER OF THE RUBIK'S CUBE GROUP IS TWENTY

SIAM JOURNAL ON DISCRETE MATHEMATICS 2013年第2期27卷 1082-1105页

作者： Rokicki, Tomas Kociemba, Herbert Davidson, Morley Dethridge, John Kent State Univ Dept Math Sci Kent OH 44242 USA Google Inc Mountain View CA 94043 USA

We give an expository account of our computational proof that every position of Rubik's Cube can be solved in 20 moves or less, where a move is defined as any twist of any face. The roughly 4.3 x 10(19) positions are partitioned into about two billion cosets of a specially chosen subgroup, and the count of cosets required to be treated is reduced by considering symmetry. The reduced space is searched with a program capable of solving one billion positions per second, using about one billion seconds of CPU time donated by Google. As a byproduct of determining that the diameter is 20, we also find the exact count of cube positions at distance 15.

关键词： group theory algorithm performance Rubik's Cube

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Parallel Newton-Krylov-Schur Flow Solver for the Navier-Stokes Equations

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AIAA JOURNAL 2013年第12期51卷 2833-2851页

作者： Osusky, Michal Zingg, David W. Univ Toronto Inst Aerosp Studies Toronto ON M3H 5T6 Canada

The objective of the present paper is to demonstrate the effectiveness of a spatial discretization based on summation-by-parts operators with simultaneous approximation terms in combination with a parallel Newton-Krylov-Schur algorithm for solving the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts operators on multiblock structured grids with simultaneous approximation terms to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using a flexible Krylov subspace iterative method with an approximate-Schur parallel preconditioner. The algorithm is verified and validated through the solution of two-dimensional model problems, highlighting the correspondence of the current algorithm with several established flow solvers. A transonic solution over the ONERA M6 wing on a mesh with 15.1 million nodes shows good agreement with experiment. Using 128 processors, the residual is reduced by 12 orders of magnitude in 86 min. The solution of transonic flow over the common research model wing-body geometry exhibits the expected grid convergence behavior. The algorithm performs well in solving flows around nonplanar geometries and flows with explicitly specified laminar-to-turbulent transition locations. Parallel scaling studies highlight the excellent scaling characteristics of the algorithm on cases with up to 6656 processors and grids with over 150 million nodes.

关键词： Navier Stokes Equations Natural Laminar Flow Spalart Allmaras Turbulence Model Reynolds Averaged Navier Stokes Discontinuous Galerkin Method Laminar to Turbulent Transition CFL3D algorithm performance Aerodynamic Shape Optimization Euler Equations

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Approach to Recovering Maneuver Accuracy in Classical Coning algorithms

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2013年第6期36卷 1884-1892页

作者： Song, Min Wu, Wenqi Pan, Xianfei Natl Univ Def Technol Dept Automat Control Changsha 410073 Hunan Peoples R China

THE coning correction is defined to account for the noncommutativity error and is a key calculation in the modern day strapdown inertial navigation attitude updating algorithms. Various algorithms have been designed and optimized to improve the accuracy of coning correction. Miller introduced the concept for optimizing coning compensation algorithms in a pure coning environment. Ignagni expanded Miller's results and showed that the optimization procedure performed in a pure coning environment also maximized coning performance in generalized vibrational environments. Using Taylor-series expansion in powers of time a new approach is presented for the coning correction algorithm design, which can recover the maneuver accuracies of known coning algorithms. In the presented approach, a previously derived coning algorithm that takes the compressed form is expanded to an uncompressed form with identical accuracy in a pure coning environment and improved accuracy under maneuvers.

关键词： Taylor Series algorithm performance Inertial Navigation Explicit Methods Quaternions

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performance of an Autonomous Multi-Maneuver algorithm for Lunar Trans-Earth Injection

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JOURNAL OF SPACECRAFT AND ROCKETS 2012年第1期49卷 165-174页

作者： Whitley, Ryan J. Ocampo, Cesar A. Williams, Jacob NASA Johnson Space Ctr Houston TX 77068 USA Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA ERC Inc ESCG Houston TX 77058 USA

Using a fully analytic initial estimate, a self-starting algorithm that constructs a flyable multiburn maneuver sequence to transfer a spacecraft from a closed low-lunar parking orbit to a desired Earth-entry state is developed and implemented. The algorithm is built to support the need for a human spacecraft to abort anytime during the mission and return automatically from a variety of lunar mission scenarios. This study presents a large set of representative test cases for algorithm evaluation, including highly constrained Earth-entry interface states that return the spacecraft to a specific landing site. For all cases, an optimal finite-burn solution is obtained successfully in computation time suitable for real-time on-board operation.

关键词： Trans Earth Injection Earth Propellant Elliptical Orbit Flight Path Angle Sequential Quadratic Programming Lift to Drag Ratio Thrust to Weight Ratio algorithm performance Search algorithm

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Loosely or Tightly Coupled Affinity for Matrix - Vector Multiplication

Loosely or Tightly Coupled Affinity for Matrix - Vector Mult...

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International Convention on Information and Communication Technology, Electronics and Microelectronics

作者： Goran Velkoski Sasko Ristov Marjan Gusev Ss. Cyril and Methodius University Faculty of Information Sciences and Computer Engineering Skopje Macedonia

ISBN: (纸本)9789532330731

Today's CPU cores usually possess private L1 and L2 cache and share L3 cache with other cores of the chip (die). Private or shared cache could have significant impact to the algorithm performance in parallel implementation, i.e. using tightly coupled CPU cores with the same last level L3 cache, or loosely coupled CPU cores with private L3 cache per chip. Private cache increases the overall cache size used during the execution. On the other side, shared cache provide implicit prefetching of the data reducing cache misses if all CPU cores of the chip use the same data. In this paper we analyze the matrix vector multiplication (MVM) algorithm performance represented with speed and speedup. We realize sequential and parallel implementation in multi-chip multi-core multiprocessor in order to determine the CPU affinity that provides the best performance for parallel implementation using the same number of tightly coupled CPU cores and their counterparts - loosely coupled CPU cores. The results show that working on loosely coupled cores with private L3 cache is better than working on tightly cores with shared last level L3 cache in the region where the problem size can be stored in the total L3 cache of loosely coupled CPU cores, but in the same time cannot be placed in only one L3 cache of tightly coupled CPU cores.

关键词： chip algorithm performance execution

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Optimal Sculling and Coning algorithms for Analog-Sensor Systems

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第3期35卷 851-860页

作者： Ignagni, Mario NavSolutions Inc Minneapolis MN 55443 USA

This paper deals with the optimization of sculling and coning algorithms in systems where the gyros and accelerometers are finite-bandwidth analog sensors that derive their incremental-angle and incremental-velocity data by numerical reconstruction. The paper provides a general treatment of the problem in which the gyros and accelerometers have known dynamic-response characteristics and in which a particular data-reconstruction scheme is used to derive incremental angles and velocities. An optimization approach is developed that allows the optimal. algorithm coefficients to be conveniently defined as the sum of the values that exist for perfect sensors and an adjustment that accounts for the composite effect of the sensor dynamic-response characteristics and data-reconstruction scheme. The optimal coefficients and the performance associated with the sculling and coning compensations for two-, three-, and four-interval algorithms are provided for nominally assumed sensor parameter values and when variations in these parameters are incorporated. Pseudosculling and pseudoconing errors resulting from relative phase shifts in the sensor outputs are analytically defined.

关键词： Inertial Sensor Accelerometer Dynamic Response Frequency Response Functions algorithm performance Microelectromechanical Systems Numerical Integration Angular Motion Inertial System Damping Ratio

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A note on circle packing

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Journal of Zhejiang University-Science C(Computers and Electronics) 2012年第8期13卷 559-564页

作者： Young Joon AHN Christoph M. HOFFMANN Paul ROSEN Department of Mathematics Education Chosun University Gwangju 501-759 Korea Department of Computer Science Purdue University West Lafayette IN 47907 USA Scientific Computing and Imaging Institute University of Utah Salt Lake City UT 84112 USA

The problem of packing circles into a domain of prescribed topology is considered. The circles need not have equal radii. The Collins-Stephenson algorithm computes such a circle packing. This algorithm is parMlelized in two different ways and its performance is reported for a triangular, planar domain test case. The implementation uses the highly parallel graphics processing unit （GPU） on commodity hardware. The speedups so achieved are discussed based on a number of experiments.

关键词： Circle packing algorithm performance Parallel computation Graphics processing unit （GPU）

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Automatic recommendation of classification algorithms based on data set characteristics

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PATTERN RECOGNITION 2012年第7期45卷 2672-2689页

作者： Song, Qinbao Wang, Guangtao Wang, Chao Xi An Jiao Tong Univ Dept Comp Sci & Technol Xian Peoples R China

Choosing appropriate classification algorithms for a given data set is very important and useful in practice but also is full of challenges. In this paper, a method of recommending classification algorithms is proposed. Firstly the feature vectors of data sets are extracted using a novel method and the performance of classification algorithms on the data sets is evaluated. Then the feature vector of a new data set is extracted, and its k nearest data sets are identified. Afterwards, the classification algorithms of the nearest data sets are recommended to the new data set. The proposed data set feature extraction method uses structural and statistical information to characterize data sets, which is quite different from the existing methods. To evaluate the performance of the proposed classification algorithm recommendation method and the data set feature extraction method, extensive experiments with the 17 different types of classification algorithms, the three different types of data set characterization methods and all possible numbers of the nearest data sets are conducted upon the 84 publicly available UCI data sets. The results indicate that the proposed method is effective and can be used in practice. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Classification algorithm automatic recommendation Classification Data set characteristics extraction algorithm performance k-Nearest Neighbors

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Strapdown Sculling algorithm Design for Sensor Dynamic Amplitude and Phase-Shift Error

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第6期35卷 1718-1729页

作者： Savage, Paul G. Strapdown Associates Inc Maple Plain MN 55359 USA

Relative phase shift between vibrating angular rate and acceleration inputs can generate significant sculling errors in strapdown computational algorithms when accompanied by inertial sensor-induced dynamic relative phase shift between gyro/accelerometer axes. This paper analyzes the problem and analytically demonstrates that all sculling algorithms can generate large errors under these conditions. Coning algorithms only use gyro inputs, hence, do not exhibit this characteristic because relative sensor-induced phase shift is not present for gyros of the same design configuration in a strapdown sensor assembly. Potential sculling algorithm solution approaches are discussed, focusing on digital sensor filtering as a simple remedy. Using a minimum integral weighted-error-squared digital prefilter design approach, the paper demonstrates that relative sensor-induced phase shift can be effectively removed so that traditionally designed sculling algorithms will accurately operate in frequency regions where input vibrations are expected.

关键词： Inertial Sensor algorithm performance Accelerometer Resonance Frequencies Strapdown Inertial Navigation System Dynamic Response Digital Filters Composite Materials Thermal Expansion Strength of Materials

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A Parameter Model of Genetic algorithm Regulating Ant Colony algorithm

A Parameter Model of Genetic Algorithm Regulating Ant Colony...

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9th IEEE International Conference on e-Business Engineering (ICEBE)/8th SOAIC/6th EM2I/6th SOKMBI/4th ASOC

作者： Wu Liu-ai Fan Wen-qing Lanzhou Jiaotong Univ Sch Math Phys & Software Engn Lanzhou 730070 Peoples R China Lanzhou Jiaotong Univ Sch Traff & Transport Lanzhou Peoples R China

ISBN: (纸本)9781467326018;9780769548098

It is difficult to determine optimal combination parameter which can make the solving performance of ant colony algorithm work better, owing to the bulkiness of parameter space and relevance among parameters. Until now, it has not owned perfect theoretical basis and been obtained mostly by repeated tests. Based on these problems, the paper finds a better combination parameter by balancing exploration and exploitation abilities of ant colony algorithm, building algorithm performance to evaluate the objective function and applying genetic algorithm to solve ant colony parameters. The experimental simulation of classical TSP problem can verify the scheme feasibility. Simulation results indicate that the model has a positive effect on determining ant colony algorithm parameters and offers a feasible scheme for selecting ant colony algorithm combination parameter.

关键词： genetic algorithm ant colony algorithm parameter selection parameter adjustment algorithm performance exploration exploitation

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