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Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation

Pavol Purcz (2001)

Kybernetika

A generalization of the spatially one-dimensional parallel pipe-line algorithm for solution of the initial-boundary-value problem using explicit difference method to the two-dimensional case is presented. The suggested algorithm has been verified by implementation on a workstation-cluster running under PVM (Parallel Virtual Machine). Theoretical estimates of the speed-up are presented.

Parallel Algorithms for Maximal Cliques in Circle Graphs and Unrestricted Depth Search

E. N. Cáceres, S. W. Song, J. L. Szwarcfiter (2010)

RAIRO - Theoretical Informatics and Applications

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of...

Parallel approximation to high multiplicity scheduling problems V I A smooth multi-valued quadratic programming

Maria Serna, Fatos Xhafa (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. To deal with the parallel...

Parallel approximation to high multiplicity scheduling problems VIA smooth multi-valued quadratic programming

Maria Serna, Fatos Xhafa (2007)

RAIRO - Theoretical Informatics and Applications

We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the unweighted model with variable processing requirements and the weighted model with identical processing requirements. These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are P-complete and hence cannot be efficiently solved in parallel unless P = NC. To deal with the parallel...

Parallel implementation of local thresholding in Mitrion-C

Tomasz Kryjak, Marek Gorgoń (2010)

International Journal of Applied Mathematics and Computer Science

Mitrion-C based implementations of three image processing algorithms: a look-up table operation, simple local thresholding and Sauvola's local thresholding are described. Implementation results, performance of the design and FPGA logic utilization are discussed.

Parallelization of artificial immune systems using a massive parallel approach via modern GPUs

Khun, Jiří, Šimeček, Ivan (2015)

Programs and Algorithms of Numerical Mathematics

Parallelization is one of possible approaches for obtaining better results in terms of algorithm performance and overcome the limits of the sequential computation. In this paper, we present a study of parallelization of the opt-aiNet algorithm which comes from Artificial Immune Systems, one part of large family of population based algorithms inspired by nature. The opt-aiNet algorithm is based on an immune network theory which incorporates knowledge about mammalian immune systems in order to create...

Progress in developing Poisson-Boltzmann equation solvers

Chuan Li, Lin Li, Marharyta Petukh, Emil Alexov (2013)

Molecular Based Mathematical Biology

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided...

Similarity relations and cover automata

Jean-Marc Champarnaud, Franck Guingne, Georges Hansel (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...

Similarity relations and cover automata

Jean-Marc Champarnaud, Franck Guingne, Georges Hansel (2010)

RAIRO - Theoretical Informatics and Applications

Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate...

Solving word equations

Habib Abdulrab (1990)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Symmetric flows and broadcasting in hypercubes

Jean-Claude Bermond, A. Bonnecaze, T. Kodate, Stéphane Pérennes, Patrick Solé (1999)

Annales de l'institut Fourier

In this paper, we propose a method which enables to construct almost optimal broadcast schemes on an n -dimensional hypercube in the circuit switched, Δ -port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured...

The CUDA implementation of the method of lines for the curvature dependent flows

Tomáš Oberhuber, Atsushi Suzuki, Vítězslav Žabka (2011)

Kybernetika

We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...

The use of fuzzy connectives to design real-coded genetic algorithms.

Francisco Herrera, Manuel Lozano, José Luis Verdegay (1994)

Mathware and Soft Computing

Genetic algorithms are adaptive methods that use principles inspired by natural population genetics to evolve solutions to search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover and mutation. A great problem in the use of genetic algorithms is premature convergence; the search becomes trapped in a local optimum before the global optimum is found. Fuzzy logic techniques may be used for solving this problem. This...

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