A novel algorithm for performing parallel, distributed computer simulations on the Internet using Internet protocol (IP) control messages is introduced. The algorithm employs carefully constructed Internet control mes...
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A novel algorithm for performing parallel, distributed computer simulations on the Internet using Internet protocol (IP) control messages is introduced. The algorithm employs carefully constructed Internet control message protocol (ICMP) packets that enable the required computations to be completed as part of the standard IP communication protocol. After providing a detailed description of the algorithm, experimental applications in the areas of stochastic neural networks and deterministic cellular automata axe discussed. As an example of the algorithm's potential power, a simulation of a deterministic cellular automaton involving 10(5) Internet-connected devices was performed.
Recent work on UNITY is directed towards replacing the relations from UNITY logic by predicated transformers. In one of his Notes on UNITY. Jayadev Misra uses UNITY logic to prove a theorem about dynamic graphs. In th...
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Recent work on UNITY is directed towards replacing the relations from UNITY logic by predicated transformers. In one of his Notes on UNITY. Jayadev Misra uses UNITY logic to prove a theorem about dynamic graphs. In this paper we use predicate transformers to prove the same theorem. We consider the elegance of the resulting proof to be an argument in favor of the use of predicate transformer.
A simple algorithm is given for the computation of the Euclidian distance from the set of black points in an N x N black and white image, for all points in the image. The running time is O(N2 log N) and O(N) extra spa...
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A simple algorithm is given for the computation of the Euclidian distance from the set of black points in an N x N black and white image, for all points in the image. The running time is O(N2 log N) and O(N) extra space is required. The algorithm is suitable for implementation on a parallel machine.
center dot Currently, domain propagation in state-of-the-art MIP solvers is single thread only. center dot The paper presents a novel, efficient GPU algorithm to perform domain propagation. center dot Challenges are d...
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center dot Currently, domain propagation in state-of-the-art MIP solvers is single thread only. center dot The paper presents a novel, efficient GPU algorithm to perform domain propagation. center dot Challenges are dynamic algorithmic behavior, dependency structures, sparsity patterns. center dot The algorithm is capable of running entirely on the GPU with no CPU involvement. center dot We achieve speed-ups of around 10x to 20x, up to 180x on favorably-large instances.
If u(x) and upsilon(x) are polynomials of degree n and m, respectively, m < n, all the coefficients of the polynomials generated by the Euclidean scheme applied to u(x) and upsilon(x) can be computed by using O (lo...
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If u(x) and upsilon(x) are polynomials of degree n and m, respectively, m < n, all the coefficients of the polynomials generated by the Euclidean scheme applied to u(x) and upsilon(x) can be computed by using O (log(3) n) parallel arithmetic steps and n(2)/log n processors over any held of characteristic O supporting FFT (Fast Fourier Transform). If the field does not support FFT the number of processors is increased by a factor of log log n;if the field does not allow division by n ! the number of processors is increased by a factor of n. This result is obtained by reducing the Euclidean scheme to computing the block triangular factorization of the Bezout matrix associated with u(x) and upsilon(x). This approach is also extended to the evaluation of polynomial gcd (greatest common divisor) over any field of constants in O (log(2)n steps with the same number of processors.
Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce...
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Underdetermined systems of equations in which the minimum norm solution needs to be computed arise in many applications, such as geophysics, signal processing, and biomedical engineering. In this article, we introduce a new parallel algorithm for obtaining the minimum 2-norm solution of an underdetermined system of equations. The proposed algorithm is based on the Balance scheme, which was originally developed for the parallel solution of banded linear systems. The proposed scheme assumes a generalized banded form where the coefficient matrix has column overlapped block structure in which the blocks could be dense or sparse. In this article, we implement the more general sparse case. The blocks can be handled independently by any existing sequential or parallel QR factorization library. A smaller reduced system is formed and solved before obtaining the minimum norm solution of the original system in parallel. We experimentally compare and confirm the error bound of the proposed method against the QR factorization based techniques by using true single-precision arithmetic. We implement the proposed algorithm by using the message passing paradigm. We demonstrate numerical effectiveness as well as parallel scalability of the proposed algorithm on both shared and distributed memory architectures for solving various types of problems.
We have discussed the multidimensional parallel computation for pseudo arc-length moving mesh schemes, and the schemes can be used to capture the strong discontinuity for multidimensional detonations. Different from t...
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We have discussed the multidimensional parallel computation for pseudo arc-length moving mesh schemes, and the schemes can be used to capture the strong discontinuity for multidimensional detonations. Different from the traditional Euler numerical schemes, the problems of parallel schemes for pseudo arc-length moving mesh schemes include diagonal processor communications and mesh point communications, which are illustrated by the schematic diagram and key pseudocodes. Finally, the numerical examples are given to show that the pseudo arc-length moving mesh schemes are second-order convergent and can successfully capture the strong numerical strong discontinuity of the detonation wave. In addition, our parallel methods are proved effectively and the computational time is obviously decreased.
The evaluation-interpolation technique of A. Toom is applied to approximate polynomial division with a remainder. This elementary method leads to the same computation (except for simple power shifts), and to the same ...
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The evaluation-interpolation technique of A. Toom is applied to approximate polynomial division with a remainder. This elementary method leads to the same computation (except for simple power shifts), and to the same record asymptotic parallel complexity estimate for this problem, O(A)(log m, m), as those of the more advanced methods of D. Bini and A. Schonhage. This approach also simplifies the approximation error analysis.
The Welsh-Powell opposition graphs have been shown to be graphs for which a certain greedy heuristic results in an optimum colouring. We propose a new characterization for this class of graphs and exploit this result ...
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The Welsh-Powell opposition graphs have been shown to be graphs for which a certain greedy heuristic results in an optimum colouring. We propose a new characterization for this class of graphs and exploit this result for the purpose of obtaining an efficient NC recognition algorithm.
In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel paramete...
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In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of various versions of MAX-SAT and provide the first constant-time algorithms parameterized either by the solution size or by the allowed excess relative to some guarantee. For the dual parameterized version where the parameter is the number of clauses we are allowed to leave unsatisfied, we present the first parallel algorithm for MAX-2SAT (known as ALMOST-2SAT). The difficulty in solving ALMOST-2SAT in parallel comes from the fact that the iterative compression method, originally developed to prove that the problem is fixed-parameter tractable at all, is inherently sequential. We observe that a graph flow whose value is a parameter can be computed in parallel and develop a parallel algorithm for the vertex cover problem parameterized above the size of a given matching. Finally, we study the parallel complexity of MAX-SAT parameterized by the vertex cover number, the treedepth, the feedback vertex set number, and the treewidth of the input's incidence graph. While MAX-SAT is fixed parameter tractable for all of these parameters, we show that they allow different degrees of possible parallelization. For all four we develop dedicated parallel algorithms that are constructive, meaning that they output an optimal assignment - in contrast to results that can be obtained by parallel meta-theorems, which often only solve the decision version.
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