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P-adic root isolation.

Thomas Sturm, Volker Weispfenning (2004)

RACSAM

We present an implemented algorithmic method for counting and isolating all p-adic roots of univariate polynomials f over the rational numbers. The roots of f are uniquely described by p-adic isolating balls, that can be refined to any desired precision; their p-adic distances are also computed precisely. The method is polynomial space in all input data including the prime p. We also investigate the uniformity of the method with respect to the coefficients of f and the primes p. Our method thus...

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...

Phenotype space and kinship assignment for the Simpson index

Bruce Litow, Dmitry Konovalov (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We investigate the computational structure of the biological kinship assignment problem by abstracting away all biological details that are irrelevant to computation. The computational structure depends on phenotype space, which we formally define. We illustrate this approach by exhibiting an approximation algorithm for kinship assignment in the case of the Simpson index with a priori error bound and running time that is polynomial in the bit size of the population, but exponential in phenotype...

Phenotype space and kinship assignment for the simpson index

Bruce Litow, Dmitry Konovalov (2007)

RAIRO - Theoretical Informatics and Applications

We investigate the computational structure of the biological kinship assignment problem by abstracting away all biological details that are irrelevant to computation. The computational structure depends on phenotype space, which we formally define. We illustrate this approach by exhibiting an approximation algorithm for kinship assignment in the case of the Simpson index with a priori error bound and running time that is polynomial in the bit size of the population, but exponential in phenotype...

Phenotypic evolution with a mutation based on symmetric α-stable distributions

Andrzej Obuchowicz, Przemysław Prętki (2004)

International Journal of Applied Mathematics and Computer Science

Multidimensional Symmetric α-Stable (SαS) mutations are applied to phenotypic evolutionary algorithms. Such mutations are characterized by non-spherical symmetry for α<2 and the fact that the most probable distance of mutated points is not in a close neighborhood of the origin, but at a certain distance from it. It is the so-called surrounding effect (Obuchowicz, 2001b; 2003b). For α=2, the SαS mutation reduces to the Gaussian one, and in the case of α=1, the Cauchy mutation is obtained. The...

Polynomials over the reals in proofs of termination : from theory to practice

Salvador Lucas (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting, etc. We...

Polynomials over the reals in proofs of termination : from theory to practice

Salvador Lucas (2010)

RAIRO - Theoretical Informatics and Applications

This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting, etc. We...

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