Fall 2005 CS 441/632/732 Parallel Computing
Homework-3
10/11/2005 1-2
Individual work only. 150 points. Due Oct 25, 2005.
1. Implement matrix-matrix multiplication with 2-D data distribution using (a) Cannon’s
algorithm (section 11.2.4, page 348) and (b) Fox’s algorithm (handout given in class).
Measure time taken for the matrix sizes 5000x5000 and 10000x10000 for the following
process grid layouts: 1x1, 2x2, and 4x4. Analyze the performance of Cannon’s algorithm vs.
Fox’s algorithm and plot the speedup plots for different process grid layouts and the two
matrix sizes. To reduce the overall execution time of the program allocate and initialize only
the required parts of the matrices in each process. Do not include the time spent in allocation
and initialization when measuring the time taken for matrix-matrix multiplication. Use BLAS
routine dgemm to perform local matrix-matrix multiplication and use an input file to
provide matrix size and process grid layout (the name of the input file must be specified as
a command line argument). Implementation of Cannon’s algorithm is optional for
undergraduate students.
Note that the problem sizes and process grid layouts where chosen such that each process
performed multiplication of square matrices. Also while measuring speedup the problem size
was fixed and the number of processes were varied. Measure the time taken by Cannon’s
algorithm and Fox’s algorithm when the matrix sizes are increased as the number of
processes are increased. Assign each process matrices of size 1000x1000 and use the
following process grid layouts: 1x1, 2x2, 3x3, and 4x4 (the corresponding global problem
sizes will be 1000x1000, 2000x2000, 3000x3000, and 4000x4000). Plot the scaled speedup
plots for both the algorithms. Use the example programs provided with the MPI tutorial as a
starting point and use MPI point-to-point and collective communications primitives for
message passing. Use the following tables to include the timing measurements:
5000x5000 10000x10000
# of
Process 1x1 = 1 2x2 = 4 4x4 = 16 1x1 = 1 2x2 = 4 4x4 = 16
Cannon
Fox
# of
Process
1x1 = 1
1000x1000
2x2 = 4
2000x2000
3x3 = 9
3000x3000
4x4 = 16
4000x4000
Cannon
Fox
General Comments:
You must implement and test these programs on the CIS cluster (Everest) and use MPI for
communication. Instructions for using the CIS cluster and submitting jobs to SGE can be found
at: http://www.cis.uab.edu/ccl/resources/everest/EverestGridNodeUserGuide.php. While
submitting to the queue you must request # of processors = # of processes, for example, for the
process grid layout 3x3, total # of processors requested = 9.
