danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2018-62-5-525-530dan-548Research ArticleМАТЕМАТИКАMATHEMATICSПлотные покрытия области вычислений гексагональными тайламиDense coverage of the computational domain by hexagonal tilesСоболевскийП. И.SobolevskyP. I.

Соболевский Павел Иосифович – доктор физико-математических наук, профессор, главный научный сотрудник.

Ул. Сурганова, 11, 220072, Минск

Sobolevsky Pavel Iosiphovich – D. Sc. (Physics and Mathematics), Professor, Chief researcher.

11, Surganov Str., 220072, Minsk

sobolevsky@im.bas-net.byБахановичС. В.BakhanovichS. V.

Баханович Сергей Викторович – кандидат физико-математических наук, ведущий научный сотрудник.

Ул. Сурганова, 11, 220072, Минск

Bakhanovich Sergei Viktorovich – Ph. D. (Physics and Mathematics), leading researcher.

11, Surganov Str., 220072, Minsk

bsv@im.bas-net.byИнститут математики Национальной академии наук БеларусиInstitute of Mathematics of the National Academy of Sciences of Belarus201829102018625525530Copyright © Соболевский П.И., Баханович С.В., 20182018Соболевский П.И., Баханович С.В.Sobolevsky P.I., Bakhanovich S.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/548

Исследованы аспекты применения гексагонального тайлинга к алгоритмам с двумерной областью вычислений. Предложено формальное определение параметризованного гексагонального тайлинга. Получены необходимые и достаточные условия плотного покрытия области вычислений гексагональными тайлами.

Представлено членом-корреспондентом Л. А. Яновичем

The hexagonal tiling in application to algorithms with a two-dimensional computational domain is investigated. A formal definition of a parametrized hexagonal tiling is proposed. Necessary and sufficient conditions for a dense coverage of the computational domain by hexagonal tiles are obtained.

Communicated by Corresponding Member Leonid A. Yanovich

тайлинггексагональный тайлингтайлоптимизация программсуперкомпьютерtilinghexagonal tilingtilecode optimizationsupercomputerПодпрограмма «Математические методы» Государственной программы научных исследований «Конвергенция 2020»Subprogram “Mathematical Methods” of the State Research Program “Convergence 2020”ReferencesXue, J. Loop Tiling For Parallelism / J. Xue. - Norwell, MA, USA: Kluwer Academic Publishers, 2000. https://doi.org/10.1007/978-1-4615-4337-4Xue J. Loop Tiling For Parallelism. Norwell, MA, USA, Kluwer Academic Publishers, 2000. https://doi.org/10.1007/978-1-4615-4337-4Parameterized tiled loops for free / L. Renganarayanan [et al.] // SIGPLAN Conference on Programming Language Design and Implementation. - New York, NY, USA: ASMPress, 2007. - P. 405-414.Renganarayanan L., Kim D., Rajopadhye S., Strout M. Parameterized tiled loops for free. SIGPLAN Conference on Programming Language Design and Implementation. New York, NY, USA, ASMPress, 2007, pp. 405-414.DynTile: Parametric Tiled Loop Generation for Parallel Execution on Multicore Processors / A. Hartono [et al.] // 24th International Parallel and Distributed Processing Symposium (2010 IPDPS Conference). - Atlanta, 2010.Hartono A., Baskaran M., Ramanujam J., Sadayappan P. DynTile: Parametric Tiled Loop Generation for Parallel Execution on Multicore Processors. 24th International Parallel and Distributed Processing Symposium (2010 IPDPS Conference), Atlanta, 2010.Bakhanovich, S. V. Parametrized Tiling: Accurate Approximations and Analysis of Global Dependences / S. V. Bakha-novich, P. I. Sobolevsky // Computational Mathematics and Mathematical Physics. - 2014. - Vol. 54, N 11. - P. 1748-1758. https://doi.org/10.1134/s0965542514110037Bakhanovich S. V., Sobolevsky P. I. Parametrized Tiling: Accurate Approximations and Analysis of Global Dependences. Computational Mathematics and Mathematical Physics, 2014, vol. 54, no. 11, pp. 1748-1758. https://doi.org/10.1134/s0965542514110037The Relation Between Diamond Tiling and Hexagonal Tiling / T. Grosser [et al.] // First International Workshop on High-Performance Stencil Computations, January 21, 2014. - Vienna, Austria, 2014.Grosser T., Verdoolaege S., Cohen A., Sadayappan P. The Relation Between Diamond Tiling and Hexagonal Tiling. First International Workshop on High-Performance Stencil Computations, Vienna, Austria, 2014.

The authors declare that there are no conflicts of interest present.