Parallel Algorithms (WISM 459), 2013/2014

Class starts on Wednesday September 18, 2013 at 10.15 hour in Utrecht. Buys Ballot building Room 017, Princetonplein 5, Uithof, Utrecht. Note the change of location!


Rob Bisseling

Time and place

Every Wednesday from 10.15-13.00 hour at Utrecht University, campus De Uithof. Location of lectures: either room 611 Hans Freudenthal building, or rooms 017, and 020 in the Buys Ballot building. First lecture: September 18, 2013. Last lecture: December 18, 2013. Please note: this is the now the correct date (see the Mastermath site). It was incorrectly written on this site as December 11. Each session consists of 2 times 45 min. lectures and one exercise class (or computer laboratory class, or question session) of 45 min. Note that class always starts at 10.15 hour, because it is part of Mastermath.

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. If you consider taking this course as part of a Bachelor's degree, please contact the teacher first about the prerequisites. 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 SARA 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 and programming is helpful. The laboratory classes will use the programming language C. If you don't know C, this may be an opportunity to learn it. You can also use C++, 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 without any change on distributed-memory machines such as Cartesius.


The examination is in the form of two assignments during the course, each with a weight of 45%, and a small written examination on the first chapter of the book with a weight of 10%. The small examination must be passed with grade 6 (out of 10) or higher. The two assignments are carried out in the exercise/laboratory class and at home. A written report must be returned 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.

Students from Utrecht must submit in hardcopy paper format and you must use LaTeX. Students from outside Utrecht University may also submit reports electronically in PDF format by email, but hardcopy is still preferred.


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. Furthermore, our student union Aeskwadraat may still have a limited number of copies. I am currently working on a second edition, and some additional material will be given to you (and will be tested on you!).

The first chapter of the book is freely available from the publisher's website, see "Sample material".

In addition, all my transparancies 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 transparencies (14 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: September 26, 2012. The transparancies are complete and they cover every section of the book. They have been converted to the Beamer macros in September 2012, and have been made up to date in the process. The old version (from 2007) in Prosper can be found here

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).

Further reading

Some weekly summaries and links

Wednesday September 18, 2013. Room 017 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;).

Computer Laboratory in adjacent rooms BBG 017 and 020 (from 12.00-13.00 hour): starting with BSPlib.
This is your first hands-on session with BSPlib. You may have to set up your accounts. Download the latest version of BSPedupack , my package of educational programs that teaches how to use BSP. Solve Exercise 1.3: try to run the benchmark, exploring your parallel environment: your own laptop and Cartesius. Change puts into gets. If you own a laptop, bring it to class, so we can install MulticoreBSP for C and check your software
Interesting links

Wednesday September 25, 2013. Room 611 Hans Freudenthal building

BSPlib, the Bulk Synchronous Parallel library

(PSC section 1.4)


(PSC sections 1.5-1.7)

Interesting links:

Exercise class
Exercise 1.2 from the book.

Wednesday October 2, 2013. Room 611 Hans Freudenthal building

Sequential LU Decomposition

(PSC sections 2.1-2.2)

Parallel LU Decomposition

(PSC section 2.3)

Exercise class
Answers to Exercise 1.2. Starting Exercise 1.7 from PSC. 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 before the deadline, Wednesday October 23, 10.15 hour.

Interesting links:

Wednesday October 9, 2013. Room 611 Hans Freudenthal building

Small examination (10.15-11.15 hour)
Test of 60 minutes on Chapter 1 of PSC. It is a closed-book examination!
Midterm Exam Parallel Algorithms 2012
Repeat Midterm Exam Parallel Algorithms 2012
Midterm Exam Parallel Algorithms 2013
Repeat Midterm Exam Parallel Algorithms 2013
Two-Phase Broadcasting

(PSC section 2.4)

Experiments with bsplu

(PSC sections 2.5-2.6)

Wednesday October 16, 2013. Room BBG 017

Sequential Recursive Fast Fourier Transform (FFT)

(PSC sections 3.1-3.2) A wonderful algorithm.

Computer Laboratory in adjacent rooms BBG 017 and 020 in the Buys Ballot Building (from 11.15-13.00 hour)
Continue with solving Exercise 1.7: write a parallel program for generating prime numbers. Run it on Cartesius. Get familiar with the interactive and batch mode.

Wednesday October 23, 2013. Room 611 Hans Freudenthal building

Sequential Nonrecursive FFT

(PSC section 3.3)

Parallel Fast Fourier Transform

(PSC section 3.4)

Exercise class

Choose a new assignment. Possibilities: solve Exercise 2.5 on Cholesky factorisation; solve Exercise 2.7 on Strassen matrix multiplication; solve Exercise 3.9 on computing π in parallel (the current world record by Kondo and Yee is 10 trillion digits); write a parallel program for counting self-avoiding walks (SAWs) on a 2D or 3D lattice. (The current world record for SAWs on the 3D cubic lattice is 36 steps.) Requests for different topics will be considered. Please try to discuss the chosen topic with teacher before mid-November.

Wednesday October 30, 2013. Room 611 Hans Freudenthal building

Repeat exam (10.15-11.15 hour)
Repeat test of 60 minutes on Chapter 1. Only if you failed the first examination or want to improve your grade. (The highest grade of the two counts.)
Weight Reduction (from 11.15 hour onwards)

(PSC section 3.5)

Program bspfft

(PSC section 3.6)

Wednesday November 6, 2013. Room 611 Hans Freudenthal building

Guest lecture Albert-Jan Yzelman (KU Leuven) from 10.15-12.00 hour. High-performance sparse matrix–vector multiplication on shared-memory architectures
Discussion of various shared-memory parallel programming interfaces, such as Cilk, OpenMP, Pthreads, and MulticoreBSP for C. Using the SpMV multiplication as an example, we will exploit the specific features of shared-memory architectures to obtain state-of-the-art performance. Slides of the lecture

Albert-Jan Yzelman is designer of the MulticoreBSP for C library that we are using.

Exercise class (12.00-13.00 hour)

Work on your new assignment. Ask anything you want to know about MulticoreBSP for C (or Java).

Wednesday November 13, 2013. Room 611 Hans Freudenthal building

Sequential sparse matrix-vector multiplication

(PSC section 4.1)

Sparse matrices and their data structures

(PSC section 4.2)

Exercise class

Work on your new assignment.

Wednesday November 20, 2013. Room 611 Hans Freudenthal building

Parallel sparse matrix-vector multiplication

(PSC section 4.3)

Cartesian matrix distributions

(PSC section 4.4)

No exercise class today
(Because of meeting Mathematics and Medicine in UMC.)

Interesting links:

Wednesday November 27, 2013. Room 611 Hans Freudenthal building

Mondriaan sparse matrix distribution

(PSC section 4.5)

New developments in 2D sparse matrix distribution
Movies of matrix partitioning, improvements in quality and speed by the medium-grain method (Mondriaan 4.0).
Exercise class

Discussion of prime number sieve, twin primes, Goldbach. Work on your new assignment.

Interesting links:

Wednesday December 4, 2013. Room BBG 017

Vector distribution

(PSC section 4.6)

Laplacian matrices

(PSC section 4.8)

Exercise/Laboratory class

Exercise 4.2, finding the optimal distribution over 8 processors for a 12 by 12 grid. Test the program of your second assignment.

Interesting links:

Wednesday December 11, 2013. Room BBG 017

Parallel graph matching
Computer Laboratory from 11.15-13.00 hour.
Please fill out the Mastermath digital evaluation form FALL 2013

Deadline second assignment January 20, 2014, 17.00 hour.

Hand in a report before the deadline. Note that it has been extended by a week! Please use the batch system of Cartesius and not the interactive system for your test runs. The interactive system is only for development. Second assignment has been graded now (February 20, 2014). Please contact me to get your grade and discuss your work with me.

Interesting links:

Wednesday December 18, 2011. Room 611 Hans Freudenthal building.

Message Passing Interface (MPI-1)

(PSC sections C.1, C.2.1-C.2.4)

Message Passing Interface (MPI-2)

(PSC Section C2.5, C3, C4)

Other courses that teach the BSP model (among others)

Last update of this page: February 20, 2014
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