Massively Parallel Algorithms - SS 2018


About this Course

There are big changes afoot. The era of increased performance from faster single cores and optimized single core programs has ended. Instead, highly parallel GPU cores, initially developed for shading, can now run hundreds or thousands of threads in parallel. Consequently, they are increasingly being adopted to offload and augment conventional (albeit multi-core) CPUs. And the technology is getting better, faster, and cheaper. It will probably even become a general computing processor on mobile devices, because it offers more processing power per energy amount.

The high number of parallel cores, however, poses a great challenge for software and algorithm design that must expose massive parallelism to benefit from the new hardware architecture. The main purpose of the lecture is to teach practical algorithm design for such parallel hardware.

Simulation is widely regarded as the third pillar of science (in addition to experimentation and theory). Simulation has an ever increasing demand for high-performance computing. The latter has received a boost with the advent of GPUs, and it is even becoming -- to some extent -- a commodity.

There are many scientific areas where the knowledge you will gain in this course can be very valuable and useful to you:

In this course, you will get hands-on experience in developing software for massively parallel computing architectures. For the first half of the lecture, there will be supervised exercises to familiarize yourself with the CUDA parallel programming model and environment. The exercises will comprise, for instance, image processing algorithms, such as you might find in Photoshop. In the second half, you can decide whether to continue with exercises, or whether to work on a small self-assignment for the rest of the cource.

Prerequisites are:

  1. A little bit of experience with C/C++ ; note that we will need just plain old C during this course, but the concept of pointers should be familiar.
  2. Liking for algorithmic thinking.

Useful, but not required, is a computer/notebook with an Nvidia GPU that is CUDA capable. You can find a list of all supported GPU's here. If you don't have access to such a computer, you are welcome to work on your assignments in our lab.

Not required are

Some of the envisioned topics (these can change during the semester):

  1. Simple parallel program models and laws
  2. Introduction to CUDA and massively parallel programming
  3. Dense matrix algorithms
  4. Parallel prefix-sum
  5. Parallel sorting
  6. Dynamic Parallelism
  7. Introduction to Thrust
  8. Parallel sphere packing
  9. Parallel Hashing
All topics are accompanied and illustrated by lots of application examples.


The following table contains the topics in more detail, the accompanying slides, and the assignments (it will be filled step-by-step after the respective lectures).

Week Topics Slides Assignments Frameworks
1. Introduction: More Moore, stream programming model, Flynn's taxonomy, overall speedup, Amdahl's law, Gustafson's law.
Fundamental Concepts of Parallel Programming 1: terminology, control flow, transfering data,
2. Fundamental Concepts of Parallel Programming 2: blocks, data flow in general multi-dimensional blocks and grids, classes in CUDA, constant memory, simplistic raytracer, warps, thread divergence, more details on the GPU architecture, warps, measuring performance, GPU/CPU synchronization, shared memory, parallel computation of the dot product PDF Assignment 1 Examples cmake
3. Fundamental Concepts of Parallel Programming 3: barrier synchronization, race conditions, document similarity, utilizing lockstepped threads instad of explicit synchronization, heat transfer simulation, double buffering pattern, texture memory, edge detection (Sobel operator), GPU's memory hierarchy, parallel histogram computation, atomic operations, pipelining host-GPU calls PDF
4. Dense matrix algorithms: matrix vector product, column major storage, AoS versus SoA, coalesced memory access, auto-tuning, arithmetic intensity, matrix-matrix multiplication, blocked matrix multiplication, All Pairs Shortest Path as matrix multiplication, PDF Assignment 2
5. Parallel prefix-sum 1: definition, simple examples, Hillis-Steele algorithm, depth & work complexity, Blelloch's algorithm, optimization, Brent's theorem & application to prefix-sum, theoretical speedup based on Brent, introduction to sequential radix sort, radix sort on the GPU, split operation, stream compaction, compressed sparse row (CSR) storage, sparse matrix-vector multiplication PDF
6. Parallel prefix-sum 2: summed area tables, increased percision for SATs, complexity of computing SAT's, depth-of-field rendering (gathering & scattering), anisotropic texture filtering, face detection with Viola-Jones. PDF Assignment 3 MatrixMul
7. Parallel sorting: comparator networks, the 0-1 principle, odd-even mergesort, bitonic sorting, work and depth complexities, (digression: adaptive bitonic sorting) PDF
8. Applications of parallel sorting: BVH construction (space filling curves, Morton codes); deformable collision detection by sweep plane approach, PCA transformation, and clustering; faster ray-tracing by coherent ray packets. PDF Assignment 4 LineOfSight
9. Dynamic Parallelism: general usage, execution model, simple example, caveats, Mariani-Silver algorithm for the Mandelbrot set, the "W" pattern for multigrids.
Random Forests 1: classification problem, simple solutions, concept of decision trees, information, entropy, information gain,
10. Random Forests 2: conditional entropy, construction of decision trees, problems of decision trees, wisdom of crowds, random forests, bootstrapping/subsampling, randomization during construction, variants of RF's, out-of-bag error estimation, parallel construction of RFs, handwritten digit recognition, body tracking using depth images. PDF
11. Introduction to thrust.
Lab meeting
PDF (NVidia) Assignment 5 Raytracer
12. Fine-grained dynamic load balancing, example application: Reyes rendering pipeline.
Parallel sphere packings: collision detection basics, inner sphere trees, bacht neural gas, parallel bounding volume hierarchy construction,
13. Parallel Hashing: application intersection of point clouds, application geometric hashing, cuckoo hashing.
Lab meeting

Some very simple examples that can serve as a starting point. They contain a makefile and should compile out-of-the-box at least under Max OS X and Linux.


The following textbooks can help review the material covered in class:

Please note that the course is not based on one single textbook! Some topics might even not be covered in any current textbook! So, I suggest you first look at the books in the library before purchasing a copy.

If you plan on buying one of these books, you might want to consider buying a used copy -- they can often be purchased for a fraction of the price of a new one. Two good internet used book shops are Abebooks and BookButler.

Grades and Points achieved by the Assignments

For taking part in a so-called "Fachgespräch" (mini oral exam), you need a grade from the assignments >= 4.0 . You can get this by successfully completing at least 40% of all asignments.

Additional Literature

Other Interesting Bits and Pieces

Gabriel Zachmann
Last modified: Wed Jul 04 15:25:42 CEST 2018