Write a parallel program to play Conway's game of life in parallel

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April 17, 2013


The goal of this programming assignment is to learn to use several advanced programming features of
MPI: virtual grid topology, creating communicators for subgrids, persistent communication, non-blocking
communication to overlap computation and communication, and derived data types. All these features must
be used to receive full points on this programming assignment, although we will give a majority of points
for a functioning implementation. We will look at the code for this assignment so your program should be
Write a parallel program to play Conway's game of life in parallel. The game takes place in a grid (or
board) of cells (or squares). Each cell can be empty or occupied. The occupied cells change from one iteration
(or generation) to the next. To go from one generation to the next, each cell in the grid is examined to see if
it will be occupied or not in the next generation. This determination is made according to the following rules.
 If an occupied cell has less than 2 neighbors, it will become empty.
 If an occupied cell has more than 3 neighbors, it will become empty.
 If an empty cell has exactly 3 neighbors, it will become occupied.
The neighbors of a cell are the 8 cells adjacent to it along the directions N, NW, W, SW, S, SE, E, NE.
Cells along an edge or at a corner have fewer neighbors.
Your program should take the following as input from a le: Two integers m and n specifying the size of
the grid (m  n grid), an integer specifying the number of generations, followed by an initial description of
the status of each grid cell (empty/occupied) given one row of the grid per line. An empty cell is indicated
with a 0 and an occupied cell is indicated with a 1. The program should run the speci ed number of gen-
erations and print the resulting grid. You are not allowed to make any assumptions on m and n. You can
assume, however, that the number of processors is either a perfect square (4, 9, 16, 25, 36, etc.) or a power
of two (2, 4, 8, 16, 32, etc.). If the number of processors is not a perfect square, the virtual grid topology
you create should be as close to a square as possible (Ex: 32 = 8  4).
The grid of life is partitioned on to the virtual grid of processors such that each processor is responsible
for a subgrid of the grid of life. The subgrids assigned to processors must be as close in size as possible.
Notice that the computational work involved in each generation is proportional to the area of the subgrid
assigned to a processor. Communication is needed to exchange the perimeter of the subgrid with neighboring
1processors. For simplicity, make the input and output parts of the program sequential. i.e., one processor
reads the input le and sends the required information to all the processors. Similarly, at the end of the
running, all processors send their subgrids to one processor which then prints the nal grid of life.
Your program must have the following features:
1. Use MPI-functions to created a virtual grid topology on the set of processors.
2. Create communicators for each row and each column and use them for communicating the edges of
the subgrid.
3. Use persistent communication because the same arguments are used in communication in each gener-
4. Use non-blocking communication to schedule requests for communication, work on internal part of
the subgrid (everything excluding the edges), wait to nish the communication, and then work on
updating the edges. This way, communication can be overlapped with computation to the maximum
extent possible.
5. Use derived datatypes to communicate the leftmost and rightmost columns of the subgrid of life as-
signed to a processor.
Also, create a sequential program to run the game of life. This will not take additional e ort because the
part of the parallel program where a subgrid of life is updated on a processor is identical to the sequential
program. The sequential program is used to measure how well we are doing in parallel.
To submit the programming assignment, turn in the following:
1. A printed copy of the program.
2. Present an analysis that derives the following:
(a) sequential run-time
(b) parallel run-time showing the computation and communication times separately
(c) an analysis of the scaling of the algorithm, i.e., keeping the eciency xed, how can we scale the
number of processors as the problem size increases? Can we scale the number of processors such
that the parallel run-time remains the same as the size of the problem is increased? Please be
brief in answering these questions.
3. Fix the number of processors to 16. Plot the speedup of a single generation as a function of the problem

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