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

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 have been 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 [1],
  • bi-partite graphs [2],
  • circulant graphs [1], and
  • multigraphs.
I also apply computational techniques to problems in this field.

Multi-objective optimisation

I have designed and implemented [3] many multi-objective integer optimisation algorithms [4,5,6] to solve such problems far faster. This is achieved through the use of parallel techniques and online communication between workers.

Combinatorial and computational topology

The Regina logo
  • Development of Regina, a mathematical software suite for 3-manifold topologists
  • Census enumeration algorithms, and their complexity [7,8]
  • Calculations of quantum invariants
  • Algorithms on triangulations
  • Spine codes of 3-manifolds [1]
  • 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. It has been improved through multiple research papers, and offers many different ways to improve running times through various tweaks and overhauls.

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

Particulars Status Pre-print
W. Pettersson and M. Ozlen. Synergistic parallel multi-objective integer programming. Submitted arXiv
W. Pettersson and M. Ozlen. Efficient Projection Partitioning for parallel multi-objective integer optimisation. Submitted arXiv
W. Pettersson and M. Ozlen. A parallel approach to bi-objective integer programming, Australian and New Zealand Industrial and Applied Mathematics Journal. Accepted, to appear arXiv
B. Burton, S. Cabello, S. Kratsch, W. Pettersson. The parameterized complexity of finding a 2-sphere in a simplicial complex, 34th International Symposium on Theoretical Aspects of Computer Science (STACS 2017) Published To appear
B. Burton and W. Pettersson. An edge-based framework for enumerating 3-manifold triangulations, 31st International Symposium on Computational Geometry (SoCG 2015) Published arXiv
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 Published arXiv
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 Published
B. Burton and W. Pettersson. Fixed parameter tractable algorithms in combinatorial topology, Lecture Notes in Computer Science vol. 8591, 2014, pp.200-311. Published arXiv
W. Pettersson. Computational Graph Theory, PhD Thesis Oct 17 2014 Accepted Self hosted
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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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