% All-Pairs Shortest Paths % David Bindel % 2015-10-19

Introduction

The Floyd-Warshall Algorithm

The Floyd-Warshall algorithm for computing all pairwise shortest path lenghs in a graph has a computational pattern much like the one for Gaussian elimination. There is a closely related algorithm which is slightly more expensive – $O(n^3 \log n)$ time in general rather than the $O(n^3)$ time required by Floyd-Warshall – but which looks very much like matrix multiplication. In this assignment, you will analyze the performance of a reference OpenMP implementation of this method, and then implement and analyze your own version using MPI.

As usual, you are allowed to use any references that you find, with appropriate citations. I know that people have worked on fast Floyd-Warshall on GPUs; you may also find prior work from when I taught the class in 2011 and used this assignment!

Your mission

You are provided with a reference OpenMP implementation (path.c). For this assignment, you should attempt three tasks:

Profiling: The current code is not particularly tuned, and there are surely some bottlenecks. Profile the computation and determine what parts of the code are slowest. I encourage you to use profiling tools (e.g. VTune Amplifier), but you may also manually instrument the code with timers.
Parallelization: The current code is parallelized with OpenMP. You should also parallelize your code using MPI, and study the speedup versus number of processors on both the main cores on the nodes and on the Xeon Phi boards. Set up both strong and weak scaling studies, varying the number of threads/processes you employ.
Tuning: You should tune your code in order to get it to run as fast as possible. For tuning, you may focus on either the OpenMP or the MPI version of the code. The computational pattern is much like that of parallel Gaussian elimination, and in addition to tuning the parallelism, I encourage you to use the tools you learned about in matrix multiply (vectorization, blocking).

The primary deliverable for your project is a report that describes your performance experiments and attempts at tuning, along with what you learned about things that did or did not work. Good things for the report include:

Profiling results
Speedup plots and scaled speedup plots
Performance models that predict speedup

In addition, you should also provide the code, and ideally scripts that make it simple to reproduce any performance experiments you've run.

Logistical notes

Timeline

As with the previous assignment, this assignment involves two stages. By Nov 3, you should submit your initial report (and code) for peer review; reviews are due by Nov 5. Final reports are due one week later (Nov 12). I hope this project is more straightforward than the shallow water equation, so that many of you will be able to wrap up early.

Peer review logistics

Since the first assignment, GitHub has added a feature to attach PDF files to issues and pull request comments. You should take advantage of this feature to submit your review as a comment on the pull request for the group you are reviewing. You should still look at the codes from the other groups, though!

Notes on MPI on the Phi boards

I have succeeded in running MPI jobs on the Phi boards, but it seems to take quite a while for jobs to start. We have also had some difficulties getting authentication working properly, and it's possible that you will run into hiccups. Please give it a try, but if you start running into trouble with MPI on the Phi, ask questions early and often -- on Piazza, so we can all figure it out together!

canondetortugas / path