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The Game Of Life

The Game Of Life. Ohad Shitrit Alon Gavra Group - 1. BGU Parallel Programming 2014. Conclusion. Parallel Analysis. Introduction:. Game of Life is a cellular automata exercise created by mathematician John H. Conway in 1970.

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The Game Of Life

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  1. The Game Of Life Ohad Shitrit AlonGavra Group - 1 BGU Parallel Programming 2014

  2. Conclusion • Parallel Analysis Introduction: • Game of Life is a cellular automata exercise created by mathematician John H. Conway in 1970. • It's not really a game in the traditional sense since the outcome is decided solely by the initial set up and there aren't any players. • The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of cellular automata • Lets play…

  3. Conclusion • Parallel Analysis The game rules: • Any live cell with fewer than two live neighbours dies, as if caused by under-population. • Any live cell with two or three live neighbours lives on to the next generation. • Any live cell with more than three live neighbours dies, as if by overcrowding. • Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

  4. Conclusion • Parallel Analysis Computational Challenges: • The game board size is NxM=L • Each cell has to be evaluated according to the set of rules • A round or “generation” takes O(L) just to evaluate. • This is an embarrassingly parallel problem • Pseudo Code for Game of Life: Bottleneck!

  5. Conclusion • Parallel Analysis Serial Solutions: • The serial solution is straight forward. • Unfortunately, when we simulate multiple generations with large boards this become a time consuming problem. • Each cell has to be individually evaluated by it’s nearby neighbours • So it becomes clear why we should turn to parallel solutions.

  6. Conclusion • Parallel Analysis Distributed Memory: • Game of life takes place on a N x M grid • Distribute the grid on z processors (domain decomposition) • Simplest way: row wise or column wise • More general approach: rectangular areas (checkerboard partitioning)

  7. Conclusion • Parallel Analysis Distributed Memory: • Initial (master) grid is in process 0 • Parts must get distributed to the other processes

  8. Conclusion • Parallel Analysis Distributed Memory: • Ghost cell: • For updating the cells, we need all the neighbours of all the • Cells • “ghost cells” around each block are necessary • This mean that cells are not continuous in memory, neither in the master nor in the worker grid

  9. Conclusion • Parallel Analysis Shared Memory Solutions: • For shared memory threads, this is almost a trivial exercise • Using a domain decomposition, put an OpenMP for pragma around one of the inner loops Here!

  10. Conclusion • ParallelAnalysis Parallel Analysis: • Amdahl’s law – strong scaling * Parallelization: Conway’s Game of Life By Aaron Weeden , Shodor Education Foundation, Inc.

  11. Conclusion • Conclusion • ParallelAnalysis • ParallelAnalysis Parallel Analysis: Parallel Analysis: • Gustafson’s Law– weak scaling * Parallelization: Conway’s Game of Life By Aaron Weeden , Shodor Education Foundation, Inc.

  12. Conclusion • Conclusion • Conclusion • Conclusion • ParallelAnalysis • ParallelAnalysis • ParallelAnalysis • ParallelAnalysis Parallel Analysis: Parallel Analysis: Parallel Analysis: Parallel Analysis: • Speed Up: • In an article we came across, the author examined 5 different programs, from the simplest serial to the sophisticated parallel program. • Using the Shared memory approach he managed to achieve a speedup of 127 times the serial program. • Speed Up: • In an article we came across, the author examined 5 different programs, from the simplest serial to the sophisticated parallel program. • Using the Shared memory approach he managed to achieve a speedup of 127 times the serial program. Based on an article by Jon Skeet: https://msmvps.com/blogs/jon_skeet/archive/2008/06/01/more-parallelisation-fun-conway-s-game-of-life.aspx Based on an article by Jon Skeet: https://msmvps.com/blogs/jon_skeet/archive/2008/06/01/more-parallelisation-fun-conway-s-game-of-life.aspx

  13. Conclusion • Conclusion • ParallelAnalysis • Parallel Analysis Conclusion: • Game of Life is the basis of much research in the field of cellular automata. As a result learning how to use parallel programming to solve the is problem has great potential in related fields of interest. • As we’ve seen the parallel solutions are easy to implement and provide improved performance. • So why not?

  14. Questions?

  15. Conclusion • Conclusion • ParallelAnalysis • Parallel Analysis References: • Jon Skeet • https://msmvps.com/blogs/jon_skeet/archive/2008/06/01/more-parallelisation-fun-conway-s-game-of-life.aspx • Dr. Dobbs • http://www.drdobbs.com/parallel/conways-game-of-life-in-parallel/240143844 • http://www.drdobbs.com/parallel/game-of-life-with-mpi/240159390 • Parallelization: Conway’s Game of Life By Aaron Weeden, Shodor Education Foundation,Inc. • Introduction to Parallel Programming with MPI, Hans Joachim Pflug, AACHEN UNIV.

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