Course Notes Parallel Algorithms (WISM 459), 2016/2017

Parallel Algorithms (WISM 459), 2016/2017


Rob Bisseling. Teaching assistant: Abe Wits.

Time and place

Every Wednesday from 10.00-12.45 hour at Utrecht University, campus De Uithof. Location of lectures: room 219 in the Buys Ballot building. First lecture: September 14, 2016. Last lecture: December 21, 2016. No class on October 12. Each session consists of 2 times 45 min. lectures and one exercise class (or computer laboratory class, or question session) of 45 min.

Intended audience

This is a Master's course which is an elective course for students of the Master's programme Mathematical Sciences of Utrecht University, part of the Scientific Computing specialisation. The course is recommended for students in Mathematics or Computer Science who are interested in scientific computing and would like to obtain a first `hands-on experience' in parallel programming. It is also highly suitable for the Honours master programme in Theoretical Physics and Mathematical Sciences and for students interested in Computational Physics. The course is part of the Dutch National Master Mastermath and hence is open for all interested master students in Mathematics in the Netherlands. Registration for everybody is through Mastermath.

Course aim

Students will learn how to design a parallel algorithm for a problem from the area of scientific computing and how to write a parallel program that solves the problem.

Learning goals

After completion of the course, the student is able to


You get 8 ECTS credit points.


Today, parallel computers are appearing on our desktops. The advent of dual-core and quad-core computers and the expected increase in the number of cores in the coming years, inevitably will cause a major change in our approach to software, such as the software we use in scientific computations. Parallel computers drastically increase our computational capabilities and thus enable us to model more realistically in many application areas.

To make efficient use of parallel computers, it is necessary to reorganise the structure of our computational methods. In particular, attention must be paid to the division of work among the different processors solving a problem in parallel and to the communication between them. Suitable parallel algorithms and systems software are needed to realise the capabilities of parallel computers.

We will discuss extensively the most recent developments in the area of parallel computers, ranging from multi-core desktop PCs, to clusters of PCs connected by switching devices, to massively parallel computers with distributed memory such as our national supercomputer Cartesius at SURFsara in Amsterdam.

The following subjects will be treated:


The course will be given in English. All reading material will be in English.


Introductory course in linear algebra. Some knowledge of algorithms. Good knowledge of a modern programming language such as C, C++, Java, or Python. Basic knowledge of C is helpful, as we will use this language in class. For a tutorial in C, if you come from another programming language, see Appendix A (pages 345-364) of "21st Century C: C Tips from the New School, 2nd Edition", by Ben Klemens, O'Reilly 2014. There are plenty of books on C; you may consider the book Practical C Programming by Steve Oualline. You can also use C++ in class, if you already know that language.


We will make use of the recently released MulticoreBSP for C software developed by Albert-Jan Yzelman. This sofware runs on shared-memory multicore PCs, and you can also run your program with only minor changes on distributed-memory machines such as Cartesius.


Recommended: Bring your own device! In certain weeks, marked below by BYOD, it is helpful to bring your own laptop, if you possess one, for use during computer laboratory sessions. Please install the MulticoreBSP library. On Macs and Linux computers this is straightforward. On Windows machines you need a UNIX emulator which runs Pthreads, and it is more difficult to get the software running. If you do not possess a laptop, perhaps your project partner does (you are allowed to work in pairs). If this fails, we will find another solution for you.

You will get access to the national supercomputer Cartesius, where you can install MulticoreBSP for C on one node, giving access to at most 24 cores for thin nodes or you can use BSPonMPI (already installed) giving access to thousands of cores.


The examination is in the form of an initial assignment (30%), a final assignment (40%), a presentation on the final assignment (15%), and homework (15%). The two assignments are carried out in the exercise/laboratory class and at home. A written report must be returned for each assignment before the deadline. Students can work individually or in pairs (but not in larger teams) on the computer programs and can hand in a single report, provided each did a fair share of the work and can account for that. Presentations will be on 14 and 21 December and will be individual. Homework must be made individually. If needed, you will have to explain your answers to the homework exercises. There will be 4 times homework to be handed in, spread over the semester, one for each chapter of the book covered (chapters 1, 2, 4, 5).

All students should submit reports for the assignments electronically in PDF format by email, to the teacher, Rob Bisseling. All homework must be handed in as hardcopy though. All students must use LaTeX for the assignments; handwritten is OK for the homework. For the first assignment, you will have to submit your parallel program to an automated testing system, Domjudge. Utrecht students (or those who had an Utrecht F-number in the past) can use their Solis-id, others should create a new account. To get everbody started in time, you will have to write a sequential prime number sieve and submit it before September 29. For questions on the Domjudge system please ask Abe Wits. Instructions for use will become available soon.


We closely follow the book Parallel Scientific Computation: A Structured Approach using BSP and MPI (PSC), by Rob H. Bisseling, Oxford University Press, March 2004. ISBN 0-19-852939-2. Please note that the book is now available by the printing-on-demand system of Oxford University Press, at the book's OUP website. If you want to buy the book, contact me first, as I can provide the participants with a discount. I am currently working on a second edition (PSC2), and some additional material will be given to you (and it will be tested on you!).

In addition, all my slides and WWW links to background material are provided through this course page. (Pointers to other relevant links are welcome!)


LaTeX sources (in Beamer) and PDFs of all my slides (18 Mbyte in gzipped tar format). The sources may be of help to other teachers who want to teach from my book. Students may find them helpful too.

Last update of the files: November 6, 2014. The slides are complete and they cover every section of the book (first edition). They have been converted to the Beamer macros in September 2012, and have been made up to date in the process. I am adding experimental results on recent computer architectures as we go.

You can also obtain the PDFs separately. Each PDF file represents one lecture of about 45 minutes.

Chapter 1: sections 2 3 4 5-7
Chapter 2: sections 1-2 3 4 5-6
Chapter 3: sections 1-2 3 4 5 6 7
Chapter 4: sections 1 2 3 4 5 6 7 8 9 10
Appendix C: Programming in BSP style using MPI, 1 (MPI-1) 2 (MPI-2).

Slides for the second edition

We will develop them as the second edition is written. Beta-versions will be provided below as they become available over the coming years, as separate links.

Further reading

Some weekly summaries and links

Wednesday September 14, 2016. Room 219 Buys Ballot building

The Bulk Synchronous Parallel model

(PSC section 1.2) What is a parallel computer? Why do we compute in parallel? The Bulk Synchronous Parallel (BSP) model by Valiant comprises an abstract machine architecture, a framework for developing algorithms, and a cost function for analysing the run time of algorithms. The BSP architecture is a set of processor-memory pairs connected by a black box communication network. BSP algorithms consist of computation supersteps and communication supersteps. Communication is costed as h-relations. The BSP cost of an algorithm is expressed in machine parameters p, g, l. The computing rate is r flop/s. Motivation of the cost model: bottlenecks at the entrance and exit of the communication network.

Parallel Inner Product Computation

(PSC section 1.3) My First Parallel Algorithm: the computation of the inner product of two vectors. Possible distributions: cyclic and block. Data distribution leads naturally to work distribution. Communication is needed to add local inner products into a global inner product. Single Program, Multiple Data (SPMD) approach: we don't want to write 400 different programs for a machine with 400 processors. One-sided communication is a great invention (in parallel computing, at least;).

Exercise class

In class: Exercise 1.2. Please hand in Exercise 1.1 as Homework 1 (HW1) on September 21, 2016.

Interesting links

Wednesday September 21, 2016.

BSPlib, the Bulk Synchronous Parallel library.

(PSC section 1.4)


(PSC sections 1.5-1.7)

Interesting links:

Computer Laboratory BYOD (from 12.00-12.45 hour): starting with BSPlib.
This is your first hands-on session with BSPlib. Download the latest version of BSPedupack, my package of educational programs that teaches how to use BSP. Note that a beta-version for the second edition will also become available soon. Preferably use this version. Solve Exercise 1.3: try to run the benchmark, exploring your parallel environment: your own laptop and Cartesius. Change puts into gets. BYOD: If you own a laptop, bring it to class, so we can install MulticoreBSP for C and check your software

Wednesday September 28, 2016.

Parallel sample sort
New material, presenting the BSP approach to sorting by regular sampling. Will become a section in Chapter 1 of PSC2.
Sequential LU Decomposition

(PSC sections 2.1-2.2)

Exercise class
Discussion of Homework 1 (HW1). Answers to Exercise 1.2. Starting Exercise 1.7 from PSC. Finish running your sequential prime number sieve on Domjudge. Design a parallel algorithm for prime number generation. Write your first parallel program. This program should generate all prime numbers below 1,000,000 in parallel. Choosing the right distribution is the name of the game.

Hand in a report on Exercise 1.7 and submit your program to the checking system, before the deadline, Wednesday October 19, 10.00 hour. Note that you can work in pairs. The format for your program is specified in the primes program specification, TBA.

Interesting links:

Wednesday October 5, 2016. Today's lectures by Jan-Willem Buurlage (CWI)

Parallel LU Decomposition

(PSC section 2.3)

Epiphany BSP
Developed by Abe Wits, Jan-Willem Buurlage, and Tom Bannink.

Slides of today's lecture by Jan-Willem Buurlage

The Epiphany chip is a 16 core chip with only 32 kb RAM per core, and incomplete documentation. It is also the world's most energy efficient processor! How to write parallel C code for such a platform? What if you want to reuse your code on a supercomputer and your laptop? We will discuss one possible solution: BSP, a parallel programming model. Learn about programming on the Parallella chip, the Epiphany architecture, BSP, streaming data structures and more!

The Parallella is like a 100$, overpowered, 18 core Raspberry Pi.

Interesting links:

Exercise class
Continue work on the prime number sieve.

Wednesday October 12, 2016.

No class because of SIAM workshop on Combinatorial Scientific Computing, Albuquerque, NM, USA

Wednesday October 19, 2016. A special day.

Two-Phase Broadcasting

(PSC section 2.4)

Experiments with bsplu

(PSC sections 2.5-2.6)

Exercise class

Choose a new assignment. Possibilities: solve Exercise 1.8 (new) on parallel sorting algorithms; solve Exercise 2.5 on Cholesky factorisation; develop a communication-avoiding LU decomposition with multiple -rank updates; write a parallel program for maximum-cardinality matching in a bipartite graph; solve Exercise 5.1 (new)write a parallel program for counting self-avoiding walks (SAWs) on a graph or a 2D or 3D lattice; solve Exercise 5.2 (new)write a parallel program for counting triangles in a social network graph. For some of the projects you could use Epiphany BSP on the Parallella board Requests for different topics will be considered. Please try to discuss the chosen topic with the teacher before mid-November.

Start working on Homework 2 (HW2) on Chapter 2, Exercise 2.2. Hand it in on October 26.

Wednesday October 26, 2016

Sequential sparse matrix-vector multiplication

(PSC section 4.1)

Sparse matrices and their data structures

(PSC section 4.2)

Exercise class
Discussion of final project.

Wednesday November 2, 2016

Parallel sparse matrix-vector multiplication

(PSC section 4.3)

Cartesian matrix distributions

(PSC section 4.4)

Exercise class
Discussion of HW2.

Wednesday November 9, 2016.

Mondriaan sparse matrix distribution

(PSC section 4.5)

Medium-grain method for sparse matrix distribution

(New material)

Exercise class

Interesting links:

Wednesday November 16, 2016.

Laplacian matrices
(PSC section 4.8)
Program bspmv and bulk synchronous message passing primitives

(PSC section 4.9)

Interesting links:

Exercise class
Homework HW3: Exercise 4.2, but with a 16 x 16 grid instead of 12 by 12. If you use LaTeX, try Tikz to produce a nice figure. Hand in November 23.

Wednesday November 23, 2016.

Parallel graph matching
(New material, PSC2 Chapter 5)

Wednesday November 30, 2016.

Guest lecture TBA

Wednesday December 7, 2016.

Parallel graph matching (continued)

(new material)

Exercise class
Homework HW4 on parallel graph matching. Register your final presentation.

Interesting links:

Wednesday December 14, 2016.

Presentations final project
Exercise class

Wednesday December 21, 2016.

More presentations final project
Exercise class
Course evaluation.

Please fill out the Mastermath digital evaluation form.

Deadline second assignment Monday January 16, 2017, 12.00 hour.

Hand in a report before the deadline. Please use the batch system of Cartesius and not the interactive system for your test runs. The interactive system is only for development.

Frequently asked questions

Other courses that teach the BSP model (among others)

Last update of this page: October 18, 2016
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