scholarly journals On Computational Hardness of Multidimensional Subtraction Games

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 71
Author(s):  
Vladimir Gurvich ◽  
Mikhail Vyalyi
Keyword(s):  
Finite Difference ◽  
Cellular Automata ◽  
Difference Set ◽  
Algorithmic Complexity ◽  
Fixed Dimension ◽  
Input Size ◽  
Speed Up

We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is EXP-complete and requires time 2Ω(n), where n is the input size. This bound is optimal up to a polynomial speed-up. The results are based on a construction introduced by Larsson and Wästlund. It relates subtraction games and cellular automata.

scholarly journals A linear speed-up theorem for cellular automata

1992 ◽  
Vol 101 (1) ◽  
pp. 59-98 ◽  
Author(s):  
J. Mazoyer ◽  
N. Reimen
Keyword(s):  
Cellular Automata ◽  
Linear Speed ◽  
Speed Up

scholarly journals Adaptive Cat Swarm Optimization Algorithm and Its Applications in Vehicle Routing Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Xiao-Fang Ji ◽  
Jeng-Shyang Pan ◽  
Shu-Chuan Chu ◽  
Pei Hu ◽  
Qing-Wei Chai ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Hybrid Algorithm ◽  
Simulation Experiments ◽  
Swarm Optimization ◽  
Routing Problem ◽  
Cat Swarm Optimization ◽  
Fixed Dimension ◽  
Speed Up ◽  
Effectiveness And Efficiency ◽  
Experimental Findings

This paper proposes a novel hybrid algorithm named Adaptive Cat Swarm Optimization (ACSO). It combines the benefits of two swarm intelligence algorithms, CSO and APSO, and presents better search results. Firstly, some strategies are implemented to improve the performance of the proposed hybrid algorithm. The tracing radius of the cat group is limited, and the random number parameter r is adaptive adjusted. In addition, a scaling factor update method, called a memory factor y, is introduced into the proposed algorithm. They can be learnt very well so as to jump out of local optimums and speed up the global convergence. Secondly, by comparing the proposed algorithm with PSO, APSO, and CSO, 23 benchmark functions are verified by simulation experiments, which consists of unimodal, multimodal, and fixed-dimension multimodal. The results show the effectiveness and efficiency of the innovative hybrid algorithm. Lastly, the proposed ACSO is utilized to solve the Vehicle Routing Problem (VRP). Experimental findings also reveal the practicability of the ACSO through a comparison with certain existing methods.

scholarly journals Cellular Automata Supportingn-Connectivity

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Biljana Stamatovic ◽  
Gregor Kosec ◽  
Roman Trobec ◽  
Xiao Xuan ◽  
Sinisa Stamatovic
Keyword(s):  
Cellular Automata ◽  
Connected Components ◽  
Cellular Automation ◽  
Speed Up

We propose a new algorithm based on cellular automation (CA) for preservingn-connectivity,n>1. The CA algorithm transforms an initial grid configuration in a grid with same number of holes but without 1-connected components. Also, maximal thinning ofn-connected components,n>1, is achieved. The grid can be used as initial for investigating properties of initial grid. Computational performances are evaluated and measured on real cases. The obtained results indicate that the proposed approach achieves comparable complexity as standard approaches; however, the speed-up and scalability of the proposed algorithm are not limited by the number of processing nodes.

Simulation of Isothermal Austenitization in Banded Pearlite Steels by Cellular Automaton

2015 ◽  
Vol 812 ◽  
pp. 465-470
Author(s):  
Gábor Karacs ◽  
András Roósz
Keyword(s):  
Free Energy ◽  
Finite Difference ◽  
Cellular Automata ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Cellular Automaton ◽  
Grain Growth ◽  
Difference Method ◽  
Transformation Process ◽  
The Real

The austenitization of steels can occur in a wide variety of initial microstructures. In this study we addressed the transformation of banded pearlite steels. Banded pearlite initial structures similar to the real ones were created. In these structures the entire transformation process was simulated whose part processes are nucleation and grain growth. The nucleation is described by a free energy based model, and the Fick II. diffusion equation by using Finite Difference Method describes the grain growth. These models have been coupled in cellular automata simulations.

scholarly journals STUDY AND MODELING 4,4'-DIAMINODIPHENYLMETHANE SYNTHESIS

2021 ◽  
Vol 64 (4) ◽  
pp. 100-103
Author(s):  
Natalia V. Menshutina ◽  
Igor V. Lebedev ◽  
Evgeniy A. Lebedev ◽  
Ratmir R. Dashkin ◽  
Mikhail V. Shishanov ◽  
...  
Keyword(s):  
Cellular Automata ◽  
High Performance ◽  
Reaction Model ◽  
Computational Experiments ◽  
Model Parameters ◽  
Suggested Model ◽  
Cellular Automata Model ◽  
Kinetic Curves ◽  
Speed Up ◽  
The Relationship

The presented work is devoted to reactions of obtaining 4,4´-diaminodiphenylmethane in the presence of a catalyst. The work describes the importance of studying 4,4´-diaminodiphenylmethane obtaining process and possibility of cellular automata approach in modelling chemical reactions. Cellular automata model which allows to predict the kinetic curves of the studied 4,4´-diaminodiphenylmethane-obtaining reaction. Model reflects two processes that are observed in the system under study - the movement of reagents under the stirring and the reaction in the presence of a catalyst. The suggested model does not use complex calculations for operation and can be implemented using high-performance parallel computing, which will speed up calculations and reduce the requirements for computing resources. The developed model was used to carry out computational experiments under various conditions. Since the model contains a number of empirical parameters, first computational experiments were carried out, which made it possible to establish the relationship between the model parameters and real values. Then, computational experiments were carried out to predict the kinetic curves of the studied reactions and were compared with the corresponding experimental data. The suggested model is suitable for predicting 4,4´-diaminodiphenylmethane-obtaining reaction kinetics. Also, model can be the part of complex multiscale modeling from the molecule level to the level of the entire apparatus.

scholarly journals Sensitivity Analysis of the Finite Difference 2-D Cellular Automata Model for Phase Transformation during Heating

2015 ◽  
Vol 55 (1) ◽  
pp. 285-292 ◽  
Author(s):  
Chandan Halder ◽  
Daniel Bachniak ◽  
Lukasz Madej ◽  
Nirupam Chakraborti ◽  
Maciej Pietrzyk
Keyword(s):  
Sensitivity Analysis ◽  
Phase Transformation ◽  
Finite Difference ◽  
Cellular Automata ◽  
Cellular Automata Model

scholarly journals Quantum interference enables constant-time quantum information processing

2019 ◽  
Vol 5 (7) ◽  
pp. eaau9674 ◽  
Author(s):  
M. Stobińska ◽  
A. Buraczewski ◽  
M. Moore ◽  
W. R. Clements ◽  
J. J. Renema ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Information Processing ◽  
Quantum Interference ◽  
Quantum Information Processing ◽  
Arbitrary Length ◽  
Input Size ◽  
Time Quantum ◽  
Speed Up ◽  
One Step ◽  
Open Question

It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis, and compression in diagnostics, astronomy, chemistry, and broadcasting build on the discrete Fourier transform. It is implemented with the fast Fourier transform (FFT) algorithm that assumes a periodic input of specific lengths, which rarely holds true. A lesser-known transform, the Kravchuk-Fourier (KT), allows one to operate on finite strings of arbitrary length. It is of high demand in digital image processing and computer vision but features a prohibitive runtime. Here, we report a one-step computation of a fractional quantum KT. The quantum d-nary (qudit) architecture we use comprises only one gate and offers processing time independent of the input size. The gate may use a multiphoton Hong-Ou-Mandel effect. Existing quantum technologies may scale it up toward diverse applications.

An Implicit Harmonic Balance Method in Graphics Processing Units for Vibrating Blades

2015 ◽  
Author(s):  
Javier Crespo ◽  
Roque Corral ◽  
Jesus Pueblas
Keyword(s):  
Finite Difference ◽  
Harmonic Balance ◽  
Graphics Processing Units ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Transonic Compressor ◽  
Speed Up ◽  
Graphics Processing

An implicit harmonic balance method for modeling the unsteady non-linear periodic flow about vibrating airfoils in turbomachinery is presented. As departing point, an implicit edge-based three-dimensional Reynolds Averaged Navier-Stokes equations solver for unstructured grids that runs both on central processing units (CPUs) and graphics processing units (GPUs) is used. The harmonic balance method performs a spectral discretization of the time derivatives and marches in pseudo-time a new system of equations where the unknowns are the variables at different time samples. The application of the method to vibrating airfoils is discussed. It is shown that a time spectral scheme may achieve the same temporal accuracy at a much lower computational cost than a Backward Finite Difference method at the expense of using more memory. The performance of the implicit solver has been assessed with several application examples. A speed-up factor of 10 is obtained between the spectral and finite difference version of the code whereas and an additional speed-up factor of 10 is obtained when the code is ported to GPUs, totalizing a speed factor of 100. The performance of the solver in GPUs has been assessed using the 10th standard aeroelastic configuration and a transonic compressor.

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