Dense coverage of the computational domain by hexagonal tiles
https://doi.org/10.29235/1561-8323-2018-62-5-525-530
Abstract
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
Supporting agencies: Subprogram “Mathematical Methods” of the State Research Program “Convergence 2020”
About the Authors
P. I. Sobolevsky
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Sobolevsky Pavel Iosiphovich – D. Sc. (Physics and Mathematics), Professor, Chief researcher.
11, Surganov Str., 220072, Minsk
S. V. Bakhanovich
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Bakhanovich Sergei Viktorovich – Ph. D. (Physics and Mathematics), leading researcher.
11, Surganov Str., 220072, Minsk
References
1. Xue J. Loop Tiling For Parallelism. Norwell, MA, USA, Kluwer Academic Publishers, 2000. https://doi.org/10.1007/978-1-4615-4337-4
2. 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.
3. 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.
4. Bakhanovich 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/s0965542514110037
5. 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.
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