Course Notes Parallel Algorithms (WISM 459), 2014/2015

Parallel Algorithms (WISM 459), 2014/2015

Final assignement has been graded (Feb. 11, 2015, 10.00 hour)


Rob Bisseling

Time and place

Every Wednesday from 10.15-13.00 hour at Utrecht University, campus De Uithof. Location of lectures: room 079 in the Buys Ballot building. First lecture: September 10, 2014. Last lecture: December 17, 2014. No class on November 12. 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. On September 17 and November 5, we will start with a lecture in BBG079 and finish with a computer laboratory in Minnaert 205.

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 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 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. Some students found the website of Harvard's CS50 course useful to quickly catch up on C, or you may consider the book Practical C Programming by Steve Oualline. 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 three homework exercises with a total weight of 10%. The two assignments are carried out in the exercise/laboratory class and at home. A written report must be returned before the deadline. For the two assignments, 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. Homework must be made individually. If needed, you will have to explain your answers to the homework exercises.

Students from Utrecht must submit reports for the assignments in hardcopy paper format. Students from outside Utrecht University may also submit reports electronically in PDF format by email, but hardcopy is still preferred. All students must use LaTeX for the assignments; handwritten is OK for the homework.


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 (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 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. I am adding experimental results on recent computer architectures as we go. 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 10, 2014. Room 079 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. Homework: Exercise 1.1 Please hand in exercise 1.1 (and not more), on September 17, 2014.

Interesting links

Wednesday September 17, 2014.

BSPlib, the Bulk Synchronous Parallel library. Room BBG079

(PSC section 1.4)


(PSC sections 1.5-1.7)

Interesting links:

Computer Laboratory in room Minnaert 205 (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

Wednesday September 24, 2014.

Sequential LU Decomposition

(PSC sections 2.1-2.2)

Parallel LU Decomposition

(PSC section 2.3)

Exercise class
Discussion of the homework. 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 15, 10.15 hour. Note that you can work in pairs.

Interesting links:

Wednesday October 1, 2014. Class from 10.15-12.15 hour.

Two-Phase Broadcasting

(PSC section 2.4)

Exercise class
Continue work on the prime number sieve. Discuss your approaches with me. Today's class finishes early, at 12.15 hour.

Wednesday October 8, 2014.

Experiments with bsplu

(PSC sections 2.5-2.6)

Sequential Recursive Fast Fourier Transform (FFT)

(PSC sections 3.1-3.2) A wonderful algorithm.

Exercise class

Continue work on the prime number sieve.

Wednesday October 15, 2014.

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 2.10 on optimising LU decomposition (try to get Cartesius higher in the Top500, improving its LINPACK performance); write a parallel program for Karp-Sipser maximum-cardinality matching in a general graph; 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 the teacher before mid-November.

Start working on Homework on Chapter 2, Exercise 2.3(a) on optimising the row swap in LU decomposition. Hand it in on October 29.

Wednesday October 22, 2014.

Program bspfft

(PSC section 3.6) Please read section 3.5 yourself as a preparation.

Sequential sparse matrix-vector multiplication

(PSC section 4.1)

Exercise class

Work on your new assignment.

Wednesday October 29, 2014

Sparse matrices and their data structures

(PSC section 4.2)

Parallel sparse matrix-vector multiplication

(PSC section 4.3)

Exercise class
Discussion of final project.

Wednesday November 5, 2014.

Cartesian matrix distributions

(PSC section 4.4)

Exercise class
Discussion on solution prime number sieve. Handback graded reports.
Computing laboratory (12.00-13.00 hour) Minnaert 205

Work on your new assignment.

Wednesday November 12, 2014. No class

because of participation in Dagstuhl Seminar High-performance Graph Algorithms and Applications in Computational Science

Wednesday November 19, 2014.

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 Homework on Chapter 2. Handback graded homework.

Interesting links:

Wednesday November 26, 2014.

Laplacian matrices

(PSC section 4.8)

Program bspmv and bulk synchronous message passing primitives

(PSC section 4.9)

Exercise class
Homework: Exercise 4.2, but with a 10 x 10 grid instead of 12 by 12. If you use LaTeX, try Tikz to produce a nice figure. Hand in December 3.

Interesting links:

Wednesday December 3, 2014.

Guest lecture Multi-BSP computing: the next step? by Albert-Jan Yzelman, KU Leuven, author of MulticoreBSP.

Abstract: Over recent years, in preparation of supercomputers that can reach a performance in the order of several exaflop per second, people have looked for new programming models. This lecture explores on why these would be required at all, by briefly re-exploring the original Bulk Synchronous Parallel (BSP) model including its currently commonly used variants (such as MPI, MapReduce, and Pregel), as well as by exploring completely different parallelisation methodologies (such as OpenMP and Cilk Plus).

The founder of BSP, Leslie Valiant, also suggested an alternative paradigm for parallel computing: the Multi-BSP model. While Multi-BSP is a hierarchical model, and while hierarchical programming is already found in contemporary high-performance computing (e.g., MPI plus OpenMP, or MPI plus CUDA), explicit hierarchical programming has its problems: it is not portable, lacks transparency, and complicates modular software design.

In this lecture, a first approach to remedy these issues, based on Multi-BSP, is presented. We illustrate the proposed framework by writing collective operations in Multi-BSP, and will briefly explore a Multi-BSP version of the fast Fourier transform as well.

Exercise class
Exploring Multi-BSP by Albert-Jan Yzelman. Please bring your laptop to class if you possess one.

Interesting links:

Wednesday December 10, 2014. Room BBG 017

Sequential graph matching

(new material)

Parallel graph matching

(new material)

Exercise class
Discussion of homework on Chapter 4.

Interesting links:

Wednesday December 17, 2011.

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)

Exercise class
Course evaluation. Discuss your final assignment.

Please fill out the Mastermath digital evaluation form. Use last year's form if needed!

Deadline second assignment January 15, 2015, 17.00 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.

All ffinal assignement have been graded now (February 11, 10.00 hour). You can come and get your report back with comments and we will discuss your work.

Other courses that teach the BSP model (among others)

Last update of this page: February 11, 2015
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