The Game Of LifeOhad ShitritAlon Gavra

Group - 1BGU

Parallel Programming2014

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 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 automataLets 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=LEach 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 problemPseudo 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 theCells“ghost cells” around each block are necessaryThis mean that cells are not continuous in memory, neither in the master nor in the worker grid

Introduction Serial Solutions Shared Memory SolutionParallel 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 Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:Amdahl’s law – strong scaling

* Parallelization: Conway’s Game of Life By Aaron Weeden , Shodor Education Foundation, Inc.

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:

* Parallelization: Conway’s Game of Life By Aaron Weeden , Shodor Education Foundation, Inc.

Gustafson’s Law– weak scaling

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:

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

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 Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Parallel Analysis:

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

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 Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Conclusion:

Introduction Serial Solutions Shared Memory SolutionParallel 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?

Questions?

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

References:

Introduction Serial Solutions Shared Memory SolutionParallel Analysis

Conclusion

Jon Skeethttps://msmvps.com/blogs/jon_skeet/archive/2008/06/01/more-parallelisation-fun-conway-s-game-of-life.aspx

Dr. Dobbshttp://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.