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Traditional heterogeneous parallel algorithms, designed for heterogeneousclusters of workstations, are based on the assumption that the absolute speedof the processors does not depend on the size of the computational task. Thisassumption proved inaccurate for modern and perspective highly heterogeneousHPC platforms. New class of algorithms based on the functional performancemodel (FPM), representing the speed of the processor by a function of problemsize, has been recently proposed. These algorithms cannot be however employedin self-adaptable applications because of very high cost of construction of thefunctional performance model. The paper presents a new class of parallelalgorithms for highly heterogeneous HPC platforms. Like traditional FPM-basedalgorithms, these algorithms assume that the speed of the processors ischaracterized by speed functions rather than speed constants. Unlike thetraditional algorithms, they do not assume the speed functions to be given.Instead, they estimate the speed functions of the processors for differentproblem sizes during their execution. These algorithms do not construct thefull speed function for each processor but rather build and use their partialestimates sufficient for optimal distribution of computations with a givenaccuracy. The low execution cost of distribution of computations betweenheterogeneous processors in these algorithms make them suitable for employmentin self-adaptable applications. Experiments with parallel matrix multiplicationapplications based on this approach are performed on local and globalheterogeneous computational clusters. The results show that the execution timeof optimal matrix distribution between processors is significantly less, byorders of magnitude, than the total execution time of the optimizedapplication.

Design and implementation of self-adaptable parallel algorithms for scientific computing on highly heterogeneous HPC platforms