Abstract
This article is devoted to an approach to solving a problem of the efficiency of parallel computing. The theoretical basis of this approach is the concept of a Q-determinant. Any numerical algorithm has a Q-determinant. The Q-determinant of the algorithm has clear structure and is convenient for implementation. The Q-determinant consists of Q-terms. Their number is equal to the number of output data items. Each Q-term describes all possible ways to compute one of the output data items based on the input data.
We also describe a software Q-system for studying the parallelism resources of numerical algorithms. This system enables to compute and compare the parallelism resources of numerical algorithms. The application of the Q-system is shown on the example of numerical algorithms with different structures of Q-determinants. Furthermore, we suggest a method for designing of parallel programs for numerical algorithms. This method is based on a representation of a numerical algorithm in the form of a Q-determinant. As a result, we can obtain the program using the parallelism resource of the algorithm completely. Such programs are called Q-effective.
The results of this research can be applied to increase the implementation efficiency of numerical algorithms, methods, as well as algorithmic problems on parallel computing systems.
- [1] . 2019. Automated construction of high performance distributed programs in LuNA system. In Parallel Computing Technologies. Lecture Notes in Computer Science, Vol. 11657. Springer, 3–9. Google ScholarCross Ref
- [2] . 2019. Designing a parallel programs on the base of the conception of Q-determinant. In Supercomputing. Communications in Computer and Information Science, Vol. 965. Springer, 565–577. Google ScholarCross Ref
- [3] . 2019. Software Q-system for the research of the resource of numerical algorithms parallelism. In Supercomputing. Communications in Computer and Information Science, Vol. 1129. Springer, 641–652. Google ScholarCross Ref
- [4] . 1985. Analysis of Parallel Numerical Algorithms.
Preprint 590 [in Russian]. Computing Center of the Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, USSR.Google Scholar - [5] . 2018. High-performance computing using the application of the Q-determinant of numerical algorithms. In Proceedings of the 2018 Global Smart Industry Conference (GloSIC’18). IEEE, Los Alamitos, CA, Article 8570160, 8 pages. Google ScholarCross Ref
- [6] . 2015. Software system for maximal parallelization of algorithms on the base of the conception of Q-determinant. In Parallel Computing Technologies. Lecture Notes in Computer Science, Vol. 9251. Springer, 3–9. Google ScholarDigital Library
- [7] . 2021. Application of the Q-determinant concept for efficient implementation of numerical algorithms by the example of the conjugate gradient method for solving systems of linear equations [in Russian]. Bulletin of the South Ural State University. Series: Computational Mathematics and Software Engineering 10, 3 (2021), 56–71. Google ScholarCross Ref
- [8] AlgoWiki. 2022. Open Encyclopedia of Parallel Algorithmic Features. Retrieved December 22, 2022 from http://algowiki-project.org/en/Open_Encyclopedia_of_Parallel_Algorithmic_FeaturesGoogle Scholar
- [9] . 2018. AlgoWiki project as an extension of the Top500 methodology. Supercomputing Frontiers and Innovations 5, 1 (2018), 4–10. Google ScholarDigital Library
- [10] . 2018. Application of the Method of Designing a Q-Effective Program for Solving the System of Grid Equations [in Russian]. Master’s thesis. School of Electronic Engineering and Computer Science. http://omega.sp.susu.ru/publications/bachelorthesis/18-Bazhenova.pdfGoogle Scholar
- [11] . 1984. Mathematical Logic. Mir, Moscow.Google Scholar
- [12] . 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness.W. H. Freeman & Co., San Francisco, CA.Google Scholar
- [13] . 1998. The Art of Computer Programming (3rd ed.).
Fundamental Algorithms , Vol. 1. Addison Wesley Longman, Boston, MA.Google Scholar - [14] . 2019. Development of a Q-Effective Program for Solving Five-Point Difference Equations by the Method of Simple Iteration and the Study of Its Dynamic Characteristics [in Russian]. Master’s thesis. School of Electronic Engineering and Computer Science. http://omega.sp.susu.ru/publications/masterthesis/2019_220_kondakovaas.pdfGoogle Scholar
- [15] . 2017. Q-Effective Implementation of the Jacobi Method for Solving SLAE on the Supercomputer “Tornado SUSU” [in Russian].Master’s thesis. School of Electronic Engineering and Computer Science. http://omega.sp.susu.ru/publications/bachelorthesis/17-Lapteva.pdf.Google Scholar
- [16] . 2018. A toolkit for the development of data-driven functional parallel programmes. In Parallel Computational Technologies. Communications in Computer and Information Science, Vol. 910. Springer, 16–30. Google ScholarCross Ref
- [17] . 2008. Scheduling problems in master-slave model. Annals of Operations Research 159, 1 (2008), 215–231.Google ScholarCross Ref
- [18] . 2014. Optimized data I/O strategy of the algorithm of parallel digital terrain analysis. In Proceedings of the 2014 13th International Symposium on Distributed Computing and Applications to Business, Engineering, and Science (DCABES’14). IEEE, Los Alamitos, CA, 34–37. Google ScholarDigital Library
- [19] . 2018. Parallel numerical algorithm for solving advection equation for coagulating particles. Supercomputing Frontiers and Innovations 5, 2 (2018), 43–54. Google ScholarDigital Library
- [20] . 1993. General purpose parallel computing. In Lectures on Parallel Computation, Alan. M. Gibbons and Paul Spirakis (Eds). Cambridge International Series on Parallel Computation. Cambridge University Press, 333–387.Google Scholar
- [21] . 2007. Parallelism granules aggregation with the T-system. In Parallel Computing Technologies. Lecture Notes in Computer Science, Vol. 4671. Springer, 293–302. Google ScholarCross Ref
- [22] . 2018. Development of a Q-Effective Program for Solving SLAE by the Gauss–Seidel Method [in Russian]. Master’s thesis. School of Electronic Engineering and Computer Science. http://omega.sp.susu.ru/publications/bachelorthesis/18-Necheporenko.pdfGoogle Scholar
- [23] . 2015. The time profit obtained by parallelization of quicksort algorithm used for numerical sorting. In Proceedings of the 2015 Science and Information Conference (SAI’15). IEEE, Los Alamitos, CA, 897–901. Google ScholarCross Ref
- [24] . 1989. Numerical Methods [in Russian]. Nauka. Main Editorial Board for Physical and Mathematical Literature, Moscow, Russia.Google Scholar
- [25] . 2018. Supercomputer modeling of parachute flight dynamics. Supercomputing Frontiers and Innovations 5, 3 (2018), 121–125. Google ScholarDigital Library
- [26] . 2015. Robust enzyme design: Bioinformatic tools for improved protein stability. Biotechnology Journal 10, 3 (2015), 344–355. Google ScholarCross Ref
- [27] . 2017. Q-Effective Co-Design of Realization of the Gauss–Jordan Method on the Supercomputer “Tornado SUSU” [in Russian].Master’s thesis. School of Electronic Engineering and Computer Science. http://omega.sp.susu.ru/publications/masterthesis/17-Tarasov.pdfGoogle Scholar
- [28] . 1990. A bridging model for parallel computation. Communications of the ACM 33, 8 (1990), 103–111.Google ScholarDigital Library
- [29] . 2017. Q-Effective Implementation of the Algorithm for Matrix Multiplication on a Supercomputer “Tornado SUSU” [in Russian].Master’s thesis. School of Electronic Engineering and Computer Science. http://omega.sp.susu.ru/publications/bachelorthesis/17-Valkevich.pdf.Google Scholar
- [30] . 1997. The V-ray technology of optimizing programs to parallel computers. In Numerical Analysis and Its Applications. Lecture Notes in Computer Science, Vol. 1196. Springer, 546–556. Google ScholarCross Ref
- [31] . 2002. Parallel Computing [in Russian]. BHV-Petersburg, St. Petersburg, Russia.Google Scholar
- [32] Accelerating embarrassingly parallel algorithm on Intel MIC. In Proceedings of the 2014 IEEE International Conference on Progress in Informatics and Computing (PIC’14).IEEE, Los Alamitos, CA, 213–218. Google ScholarCross Ref
- [33] . 2016. Research on parallel algorithms for calculating static characteristics of electromagnetic relay. In Proceedings of the 2016 IEEE 11th Conference on Industrial Electronics and Applications (ICIEA’16).IEEE, Los Alamitos, CA, 1421–1425. Google ScholarCross Ref
Index Terms
- Investigation and Implementation of Parallelism Resources of Numerical Algorithms
Recommendations
Space-efficient implementation of nested parallelism
Many of today's high level parallel languages support dynamic, fine-grained parallelism. These languages allow the user to expose all the parallelism in the program, which is typically of a much higher degree than the number of processors. Hence an ...
Space-efficient implementation of nested parallelism
PPOPP '97: Proceedings of the sixth ACM SIGPLAN symposium on Principles and practice of parallel programmingMany of today's high level parallel languages support dynamic, fine-grained parallelism. These languages allow the user to expose all the parallelism in the program, which is typically of a much higher degree than the number of processors. Hence an ...
Comments