Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Introduction:  Game of Life is a cellular automata exercise created by mathematician John H. Conway in  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 automatacellular automata  Lets play…

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion 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.

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion 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!

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion 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.

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion 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)

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Distributed Memory:  Initial (master) grid is in process 0  Parts must get distributed to the other processes

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion 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

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion 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!

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis:  Amdahl’s law – strong scaling * Parallelization: Conway’s Game of Life By Aaron Weeden, Shodor Education Foundation, Inc.

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis: Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis: * Parallelization: Conway’s Game of Life By Aaron Weeden, Shodor Education Foundation, Inc.  Gustafson’s Law– weak scaling

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis: Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis: Based on an article by Jon Skeet: 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. Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis: Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Parallel Analysis: Based on an article by Jon Skeet: 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.

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion Conclusion: Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution 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?

Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion References: Introduction Computational Challenges Serial Solutions Distributed Memory Solution Shared Memory Solution Parallel Analysis Conclusion  Jon Skeet game-of-life.aspx  Dr. Dobbs  Parallelization: Conway’s Game of Life By Aaron Weeden, Shodor Education Foundation,Inc.  Introduction to Parallel Programming with MPI, Hans Joachim Pflug, AACHEN UNIV.