William Pettersson

William Pettersson

Headshot of William Pettersson
William Pettersson, Research Fellow
School of Science, RMIT University ,
Melbourne, Victoria, Australia

Email: william@ewpettersson.se
XMPP: william@ewpettersson.se
Languages: English, Swedish

About Me

I am a mathematician, and currently employed as a research fellow at RMIT. My research has taken me from graph decompositions through combinatorial toplogy, and I am currently looking at using linear and integer programming solutions to solve problems in computational topology.

I also have a strong interest in computing, reaching from the algorithms I use in my research to the complex world of information security. I have practical experience with coding at all levels, from assembly for the HC12 through C, and C++ all the way to Python, PHP and Perl. Details on some of these projects are available below.

As a student I have played integral roles in the organisation of various social functions as a part of the Mathematics Students Society. I was a member of the Host Scientific Committee for the 2013 International Olympiad in Informatics and was involved with the Queensland Informatics & Programming Club to train high school students in informatics.
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Research Interests

Graph Decompositions

A decomposition of K7 I study the existence of decompositions and factorisations of
  • complete graphs,
  • circulant graphs, and
  • multigraphs.
I also apply computational techniques to problems in this field.

Combinatorial and computational topology

The Regina logo
  • Development of Regina, a mathematical software suite for 3-manifold topologists
  • Census enumeration algorithms, and their complexity
  • Spine codes of 3-manifolds
  • Properties of Pachner graphs
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Software projects

Optimisation

moip_aira is an implementation of a parallel multi-objective integer programming algorithm that aims for perfect parallelisation. This project is under active development, but as yet has no official releases and as such may be broken at various releases.

Graph theory

graphlib is a library of graph decomposition techniques that were used to find various decompositions and factorisations which were in turn used to solve the cycle decomposition problem for complete graphs.

rook_decomp is a small program that is currently trying to find a decomposition of the complete bipartite graph on 2n vertices into copies of the rook graph Kn.

Other

My Github page lists many other projects that I have at some point worked on.

Combinatorial and computational topology

The Regina logo
Regina - Software for 3-manifold topology and normal surface theory

I am one of the developers of Regina, a suite of mathematical software for 3-manifold topologists. It focuses on the study of 3-manifold triangulations and normal surfaces. I also maintain the Gentoo packages for Regina. For official downloads for other distributions, see http://regina.sourceforge.net.

Gentoo packages for Regina are available in a layman overlay. Once layman has been installed, you can install the overlay by running # layman -a regina-gentoo. You will then be able to install Regina with # emerge regina. Note that version 9999 of Regina in the overlay will always update to the latest GIT revision, which may or may not work at any given time.

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Publications

Published
  1. W. Pettersson. Computational Graph Theory, PhD Thesis Oct 17 2014; (Available online)
  2. B. Burton and W. Pettersson. Fixed parameter tractable algorithms in combinatorial topology, Lecture Notes in Computer Science vol. 8591, 2014, pp.200-311. (Publisher, arXiv)
  3. D. Bryant, P. Danziger and W. Pettersson. Bipartite 2-factorisations of complete multipartite graphs, Journal of Graph Theory vol. 78, issue 4. April 2015;, pp.287-294 doi: 10.1002/jgt.21806 (Publisher)
  4. D. Bryant, D. Horsley, and W. Pettersson. Cycle decompositions V: Complete graph into cycles of arbitrary lengths, Proceedings of the London Mathematical Society 2014; doi: 10.1112/plms/pdt051 (Publisher, arXiv)
  5. B. Burton and W. Pettersson. An edge-based framework for enumerating 3-manifold triangulations, SoCG 2015: 31st International Symposium on Computational Geometry, Leibniz International Proceedings in Informatics vol. 34, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2015, pp. 270-284. (Publisher, arXiv)
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Teaching

At The University of Queensland
As a teaching assistant:
  • 2014 : MATH4303 Advanced Combinatorics
  • 2011-2014 : MATH3301 Graph Theory and Design Theory
  • 2010-2014 : MATH3302 Coding and Cryptography
  • 2010-2014 : MATH1061 Discrete Mathematics
  • 2011-2013 : MATH3500 Problems and Applications in Modern Mathematics
  • 2011 : MATH4302 Combinatorial Designs
  • 2010 : MATH3306 Set Theory and Logic
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