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CSE 6230, Fall 2014: Lab 4: Broadcast algorithms (DUE: Th Oct 2)

In this hands-on lab, you will use Message Passing Interface (MPI) point-to-point operations to implement the two broadcast algorithms we discussed in the previous class. The first of these uses a tree-based approach, which is latency-optimal; the second uses a scatter + all-gather approach, which is bandwidth-optimal (to within a constant factor).

Recall that MPI provides a portable interface for parallel tasks running on different nodes of a cluster or supercomputer to send messages to each other.

As usual, you may work in teams of up to two people per team. In addition to committing your code changes and data files, please also create a PDF file called README.pdf, which should contain:

  • yours and your partner's names;
  • answers to the 5 questions in this assignment;
  • plots of the data you collect below.

Part 0a: Setting up MPI for your environment

Start by logging into Jinx and setting up your environment so that the code we are providing will compile and run. In particular, this lab's experiments rely on a particular version of the GCC compiler as well as the MPI communication library discussed in the previous class.

Set up your shell environment for compiling and running MPI programs. Add the following lines to your .bashrc file in your home directory. (Go ahead and create this file if it does not already exist.)

# Add these lines to ~/.bashrc, if not there already:
if [ -f /etc/bashrc ]; then
  source /etc/bashrc
fi

# Add this line for MPI support
source /nethome/rvuduc3/local/jinx/setup-mpi.sh

You may also need to add the following line to .bash_profile, also in your home directory. (Again, create this file if it does not already exist.)

# Add these lines to ~/.bash_profile, if not there already:
if [ -f ~/.bashrc ] ; then
  source ~/.bashrc
fi

Once you've made these changes, log out and log back in for this setup to take effect. If it worked, then the command

which mpirun

should return the string, /nethome/rvuduc3/local/jinx/openmpi/1.6.2-mt--gcc4.7.2/bin/mpirun.

For future reference, the above sets up a version of OpenMPI, not to be confused with OpenMP. The other major open-source MPI implementation is MPICH. Many of the major cluster, supercomputer, and networking vendors [1] provide their own implementations of MPI as well.
[1]Examples of vendors include Intel, IBM, Cray, and Mellanox, among others.

Part 0b: Obtaining this week's code

Use the same fork-checkout procedure from Lab 1. [2] The repo you want is gtcse6230fa14/lab4. As a reminder, the basic steps to get started are:

  1. Log into your Bitbucket account.
  2. Fork the code for this week's lab into your account. The URL is https://bitbucket.org/gtcse6230fa14/lab4.git . Be sure to rename your repo, appending your Bitbucket ID. Also mark your repo as "Private" if you do not want the world to see your commits.
  3. Check out your forked repo on Jinx. Assuming your Bitbucket login is MyBbLogin and assuming that you gave your forked repo the same name (lab4-MyBbLogin), you would on Jinx use the command:
git clone https://MyBbLogin@bitbucket.org/MyBbLogin/lab4-MyBbLogin.git

(Alternatively, if you figured out how to do password-less checkouts using ssh keys, you might use the alternative checkout style, git clone git@bitbucket.org:MyBbLogin/lab4--MyBbLogin.git.)

If it worked, you'll have a lab4-MyBbLogin subdirectory that you can start editing.

The code we have provided includes these files:

  • serial.c: An implementation of a na├»ve broadcast algorithm.
  • tree.c: A latency-optimal implementation of a minimum spanning tree-based algorithm.
  • bigvec.c: A partial implementation of the scatter + all-gather algorithm, which you will complete and compare against the tree-based algorithm.
  • A bunch of other files, described below as needed.
[2]https://bitbucket.org/gtcse6230fa14/lab1/wiki/Home

Part 1: Creating a communication model for point-to-point operations

Your goal is to devise, model, and implement algorithms for broadcasting the data from one MPI process to all others, using _only_ the MPI point-to-point communication operations, such as MPI_Send, MPI_Recv, or their non-blocking counterparts, MPI_Isend, MPI_Irecv, and MPI_Wait.

The file serial.c implements a "naive" broadcast algorithm. The data resides initially on MPI rank 0. This rank sends its data to each of the other processes, one by one. Inspect serial.c and verify that the bcast() routine implemented therein implements such a scheme.

We ran this benchmark on the Jinx cluster. The results appear in the graph below. More specifically, we show the average time per broadcast (y-axis) as a function of the size of the data size (x-axis).

Figure1

Figure 1: Performance of the naive algorithm on Jinx. Note that the x-axis is on a \(\log_2\) scale, the y-axis on a \(\log_{10}\) scale.

Question 1: Assume that the time \(T(n)\) to send a message of size \(n\) words is \(T_{\mbox{msg}}(n) = \alpha + \beta n\), where \(\alpha\) is the message latency, in units of time, and \(\beta\) is the inverse bandwidth, in units of time per word. Then, use the data of Figure 1 to estimate the values of \(\alpha\) and \(\beta\). You may either eyeball the plot or use the raw data used to generate these plots, which appear at the following links for two processors (serial-2.dat), four processors (serial-4.dat), and eight processors (serial-8.dat). Explain how you derived your estimate and report \(\alpha\) in microseconds and \(\beta\) in microseconds per byte. (Note that the plot shows message sizes along the x-axis in bytes, kibibytes, and mebibytes.)

The raw data is stored in a tab-delimited files. Each file has four columns. The first column is the number of MPI processes (ranks). The second column is the size of the data being broadcast, in Bytes. The third column is the average time to perform the broadcast, in seconds. The fourth column is the number of timing trials used to compute the average. (You can basically ignore the last column.)

Part 2: Modeling the "small" and "large" vector broadcast algorithms

In class, we described two algorithms for broadcast. The first algorithm is a minimum spanning tree approach. We argued this method is good for small messages because it is optimal with respect to latency (number of messages). The other uses a two-stage "scatter" plus "all-gather" technique, which we argued was good for large messages ("big vectors") because it trades a higher latency component for an asymptotically-optimal bandwidth component.

Look at the bcast() code in tree.c. Convince yourself that it implements a minimum spanning tree algorithm like the one described in class. Note that it assumes a power-of-two number of processes and, furthermore, that the number of processes divides the number of data elements.

Question 2: Using your model of message time from Question 1, write down an analytical model of the time to execute the tree-based algorithm.

Running the tree-based algorithm

Let's see how accurately the model from Question 2 predicts actual execution time by running the tree-based algorithm. We have provided a Makefile to simplify compiling and running this code (and the others we will use in this lab).

To compile, simply execute:

make

If it succeeds, it will produce the binary program named tree.

We have provided Makefile rules that make it easy to run this code and generate a performance plot like that shown in Figure 1 (above). The command,

make pbs ALG=tree P=2 ; qstat -a

will submit a batch job that runs the tree program with two nodes (P=2) and various message sizes. Go ahead and run this command now; the qstat -a part peeks at the job queue to verify the job is in the queue. (Repeat qstat -a to monitor the progress of this job.) Once it begins running, it should complete in about a minute and generate a file called, tree-2.dat, which will have the same format as the serial-?.dat files above. Repeat this command with P=4 and P=8 to collect data for the tree-based algorithm running with four and eight nodes, respectively.

Once you've collected this data, you can generate a plot by executing the command,

make plot-alg ALG=tree

This will run a gnuplot script to plot the tree-2.dat, tree-4.dat, and tree-8.dat data. If successful, it will create a file called tree.png. You can download or use display to see it. [3]

[3]You must have X11-forwarding enabled in order to use the display command. If you can't figure out how to do it, download the .png file and view it locally.

Question 3: Compare these data to your model from Question 2. How well do they agree?

Implementing the "scatter + all-gather" approach for "big vectors"

Take a look at bigvec.c, which is a partial implementation of the algorithm designed for large vectors. In particular, we've provided the "scatter" step; you will need to complete the "all-gather" step.

Question 4: Complete the "all-gather" code, using only point-to-point MPI operations (either blocking or non-blocking, as you wish). See the notes below on compiling and testing your code. You may make the same assumptions as we do in the tree-based algorithm: power-of-two number of processes and the number of processes evenly dividing the message length.

To compile your implementation, you can use the command,

make bigvec

This will generate the executable, bigvec. You may choose to test it interactively on a single node; once you've gotten it debugged, perform a timing run on eight nodes using the command,

make pbs ALG=bigvec P=8

When this run succeeds, it will create a data file called, bigvec-8.dat.

Question 5: Plot the serial-8.dat, tree-8.dat, and bigvec-8.dat together. (See below for a make rule we have provided that uses gnuplot script to do it; alternatively, use any plotting software you wish.) You should see that the tree-based method is faster for "small" messages, whereas the scatter+allgather method if faster for "large" messages. What is the cross-over point (message size) between the tree and scatter+allgather methods?

To use the gnuplot script we have provided to generate this plot, use make to run it as follows:

make plot-all P=8

Turning in your solution

Once you are satisfied, be sure you add and commit your code and all of the *.dat files, as well as any images you produced. Document your work, including the answers to the questions above, in a README.pdf file as directed at the top of this page. Finally, transfer these to the gtcse6230fa14 account by the deadline.

Updated