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A decentralized convergence detection algorithm for asynchronous parallel iterative algorithms

IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2005年第1期16卷 4-13页

作者： Bahi, JM Contassot-Vivier, S Couturier, R Vernier, F Univ Franche Comte Lab Informat LIFC FRE CNRS 2661IUT Belfort Montbeliard F-90016 Belfort France

We introduce a theoretical algorithm and its practical version to perform a decentralized detection of the global convergence of parallel asynchronous iterative algorithms. We prove that, even if the algorithm is completely decentralized, the detection of global convergence is achieved on one processor under the classical conditions. The proposed algorithm is very useful in the context of grid computing in which the processors are distributed and in which detecting the convergence on a master processor may be penalizing or even impossible as in Peer to Peer computation frameworks. Finally, the efficiency of the practical algorithm is illustrated in a typical experiment.

关键词： parallel iterative algorithms asynchronism convergence detection

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An approach to optimise the energy efficiency of iterative computation on integrated GPU-CPU systems

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JOURNAL OF SUPERCOMPUTING 2017年第1期73卷 114-125页

作者： Garzon, E. M. Moreno, J. J. Martinez, J. A. Univ Almeria CeiA3 Dept Informat Almeria 04120 Spain

Currently, the energy efficiency of computational systems is of paramount relevance. In this work, an approach for improving energy efficiency is proposed in the context of the iterative computation on integrated GPU-CPU systems. The proposal, referred to as E-ADITHE, combines iterative procedures with: (1) a heuristic scheme for processing units selection according to the estimation of energy efficiency and (2) the load balancing on heterogeneous processors. There is a wide variety of iterative algorithms related to science and engineering which can take advantage of E-ADITHE. The Beltrami filter has been selected as a representative example of such procedures and its OpenCL version has been used to validate E-ADITHE. The analysis of the results shows that E-ADITHE improves automatically the energy efficiency of parallel iterative algorithm on modern heterogeneous processors.

关键词： Energy efficiency Heterogeneous processors parallel iterative algorithms Integrated CPU-GPU

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Congestion control for asynchronous parallel computing on workstation networks

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parallel COMPUTING 1997年第13期23卷 1855-1875页

作者： Heddaya, A Park, K Boston Univ Dept Comp Sci Boston MA 02215 USA Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA

Asynchronous parallel computing can result in high message generation rates, thus triggering network congestion. We characterize the communication requirements of a large class of supercomputing applications falling under the category of fixed-point problems amenable to solution by parallel iterative methods. In particular, we concentrate on asynchronous iterative algorithms whose communication/computation ratio is especially high resulting in degraded effective throughput if communication is not managed properly. Second, we show the effects of network contention and asynchrony on application performance in a local-area network environment and investigate methods of solution. Our approach is based on a congestion control algorithm called 'warp control' whose adaptive properties are exploited to yield significant performance enhancements when network contention is high. Although tested in a LAN environment for experimental control purposes, our solution follows the end-to-end paradigm and refrains from exploiting special MAC-layer properties to achieve applicability to general WAN environments. Third, we provide a framework wherein efficient congestion control can be facilitated, encompassing methods acting at the application layer as well as the transport/network layer, with emphasis on application-driven control. We conclude with a discussion of our experimental results and special issues arising in high-bandwidth ATM networks. (C) 1997 Elsevier Science B.V.

关键词： distributed parallel computing congestion control parallel iterative algorithms communication architecture

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Automatic tuning of iterative computation on heterogeneous multiprocessors with ADITHE

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JOURNAL OF SUPERCOMPUTING 2011年第2期58卷 151-159页

作者： Martinez, J. A. Garzon, E. M. Plaza, A. Garcia, I. Univ Almeria Dept Comp Architecture & Elect Almeria 04120 Spain Univ Extremadura Dept Technol Comp & Commun Caceres 10071 Spain

This work studies the problem of balancing the workload of iterative algorithms on heterogeneous multiprocessors. An approach, called ADITHE, is proposed and evaluated. Its main features are: (1) using a homogeneous distribution of the workload on the heterogeneous system, the speed of every node is estimated during the first iterations of the algorithm;(2) according to the speed of every node, a new workload distribution is carried out;(3) the remaining iterations of the algorithm are executed. The result of this workload redistribution is that the execution times for every iteration at every node are similar and, consequently, the penalties due to synchronization between nodes at every iteration are mostly eliminated. This approach is appropriate for iterative algorithms with similar workload at every iteration, and with a relevant number of iterations. The high portability of ADITHE is guaranteed because the estimation of speed of nodes is included in the execution of the parallel algorithm. There is a wide variety of iterative algorithms related to science and engineering which can take advantage of ADITHE. An example of this kind of algorithms (morphological processing of hyperspectral images) is considered in this work to evaluate its performance when ADITHE is applied. The analysis of the results shows that ADITHE significantly improves the performance of parallel iterative algorithms on heterogeneous platforms.

关键词： parallel iterative algorithms Heterogeneous multiprocessors

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Asynchronous grid computation for American options derivatives

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ADVANCES IN ENGINEERING SOFTWARE 2013年 60-61卷 136-144页

作者： Chau, M. Couturier, R. Bahi, J. Spiteri, P. Adv Solut Accelerator F-34170 Castlenau Le Lez France IUT Belfort Montbeliard FEMTO ST Inst F-90016 Belfort France ENSEEINT IRIT F-31071 Toulouse France

In relation with the mathematics of financial applications, the present study deals with the solution of the time dependent obstacle problem defined in a three-dimensional domain;this problem arises in the pricing of American options derivatives. In order to solve very quickly large scale algebraic systems derived from the discretization of the obstacle problem, the parallelization of the numerical algorithm is necessary. So, we present parallel synchronous, and more generally asynchronous, iterative algorithms to solve this problem. For the considered problem, arguments implying the convergence of parallel synchronous and asynchronous algorithms are given in a general framework. Finally, computational experiments on GRID'5000, the French national grid, are presented and analyzed. They allow us to compare both synchronous and asynchronous versions with local and distributed clusters and to show the interest of such methods in the context of grid computing. (C) 2012 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

关键词： parallel iterative algorithms Asynchronous iterations Obstacle problem Grid computing American options Projected relaxation method

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Dynamic load balancing and efficient load estimators for asynchronous iterative algorithms

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IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2005年第4期16卷 289-299页

作者： Bahi, JM Contassot-Vivier, S Couturier, R Univ Franche Comte Lab Informat LIFC FRE CNRS 2661IUT Belfort Montbeliard F-90016 Belfort France

In a previous paper [1], we have shown the very high power of asynchronism for parallel iterative algorithms in a global context of grid computing. In this article, we study the interest of coupling load balancing with asynchronism in such algorithms. After proposing a noncentralized version of dynamic load balancing which is best suited to asynchronism, we verify its efficiency by some experiments on a general Partial Differential Equation (PDE) problem. Finally, we give some general conditions for the use of load balancing to obtain good results with this kind of algorithm and discuss the choice of the residual as an efficient load estimator.

关键词： parallel iterative algorithms asynchronism load-balancing

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parallel solution of the obstacle problem in Grid environments

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INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2011年第4期25卷 488-495页

作者： Chau, M. Couturier, R. Bahi, J. Spiteri, P. Adv Solut Accelerator F-34170 Castlenau Le Lez France LIFC EA 4269 F-90016 Belfort France ENSEEIHT IRIT F-31071 Toulouse France

The present study deals with the solution of the obstacle problem defined in a three-dimensional domain. In order to solve a large-scale obstacle problem, the use of parallelism is necessary. In this work we present a parallel synchronous iterative algorithm to solve this problem and its asynchronous version. For the considered problem, the convergence of parallel synchronous and asynchronous algorithms is analysed in a general framework. Finally, computational experiments on GRID'5000, the French national grid, are presented and analysed. They allow us to compare both synchronous and asynchronous versions with local and distributed clusters.

关键词： asynchronous iterations grid computing obstacle problem parallel iterative algorithms Richardson method

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CONVERGENCE OF A parallel JACOBI-TYPE METHOD

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1983年第3-4期14卷 371-384页

作者： MISSIRLIS, NM Department of Applied Mathematics University of Athens Panepistimiopolis 621 Athens Greece

A relaxed Jacobi-type iterative scheme is presented for solving linear algebraic systems. The method possesses a high level of parallelism and can be implemented on a multiprocessor system with or without synchronisation. The convergence region of the relaxation parameter is determined under the condition that the Jacobi iteration matrix possesses real eigenvalues. However, when the method is applied to consistently ordered systems, it is preferrable to let the parameter equal to unity and use Conjugate Gradient methods [3] to further increase the convergence rate.

关键词： parallel iterative algorithms Linear systems Relaxation techniques AMS(MOS): 65F10 C.R: 5.14

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Grid solution of problem with unilateral constraints

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NUMERICAL algorithms 2017年第4期75卷 879-908页

作者： Chau, M. Laouar, A. Garcia, T. Spiteri, P. IRT SystemX 8 Ave Vauve F-91120 Palaiseau France Univ Annaba Fac Sci Lab LANOS Dept Math BP 12 Annaba 23000 Algeria UMR CNRS 5505 IRIT ENSEEIHT 2 Rue Camichel BP 7122 F-31071 Toulouse France UVSQ PRISM 45 Ave Etats Unis F-78035 Versailles France

The present study deals with the solution of a problem, defined in a three-dimensional domain, arising in fluid mechanics. Such problem is modelled with unilateral constraints on the boundary. Then, the problem to solve consists in minimizing a functional in a closed convex set. The characterization of the solution leads to solve a time-dependent variational inequality. An implicit scheme is used for the discretization of the time-dependent part of the operator and so we have to solve a sequence of stationary elliptic problems. For the solution of each stationary problem, an equivalent form of a minimization problem is formulated as the solution of a multivalued equation, obtained by the perturbation of the previous stationary elliptic operator by a diagonal monotone maximal multivalued operator. The spatial discretization of such problem by appropriate scheme leads to the solution of large scale algebraic systems. According to the size of these systems, parallel iterative asynchronous and synchronous methods are carried out on distributed architectures;in the present study, methods without and with overlapping like Schwarz alternating methods are considered. The convergence of the parallel iterative algorithms is analysed by contraction approaches. Finally, the parallel experiments are presented.

关键词： Variational inequality parallel iterative algorithms Asynchronous iterations Unilateral constraints problem Grid computing Fluid mechanics

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parallel asynchronous Schwarz and multisplitting methods for a nonlinear diffusion problem

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NUMERICAL algorithms 2003年第1-4期33卷 461-474页

作者： Spiteri, P Miellou, JC El Baz, D Inst Natl Polytech Toulouse ENSEEIHT IRIT LIMA F-31071 Toulouse France Univ Franche Comte UFR Sci & Tech Dept Math F-25030 Besancon France CNRS LAAS F-31077 Toulouse France

parallel asynchronous subdomain algorithms with flexible communication for the numerical solution of nonlinear diffusion problems are presented. The discrete maximum principle is considered and the Schwarz alternating method and multisplitting methods are studied. A connection is made with M-functions for a classical nonlinear diffusion problem. Finally, computational experiments carried out on a shared memory multiprocessor are presented and analyzed.

关键词： parallel iterative algorithms asynchronous iterations Schwarz alternating method multisplitting method subdomain methods boundary value problems

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