Benjamin Burton — Publications

Last updated: 7 March 2016

Download links are offered in the right-hand column. These include links to the published versions on journal/proceedings websites, and also self-archived versions on my own website for readers who cannot access the publishers' materials.

Preprints
Courcelle’s theorem for triangulations (with Rodney G. Downey)
Preprint, arXiv:1403.2926, March 2014.
arXiv
Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations
Journal version: Preprint, arXiv:1110.6080, October 2011. arXiv
Conference version: The Pachner graph and the simplification of 3-sphere triangulations
SCG ’11: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry
ACM, 2011, pp. 153–162.
Publisher
Self-archive
In press
Computational geometric and algebraic topology (with Herbert Edelsbrunner, Jeff Ericsson and Stephan Tillmann) (ed.)
(Invited but not reviewed)
Oberwolfach Reports, to appear.
Publisher
Finding non-orientable surfaces in 3-manifolds (with Arnaud De Mesmay and Uli Wagner)
SoCG 2016: 32nd International Symposium on Computational Geometry
To appear, arXiv:1602.07907, February 2015.
arXiv
On the complexity of immersed normal surfaces (with Éric Colin de Verdière and Arnaud de Mesmay)
Journal version: Geometry & Topology, to appear, arXiv:1412.4988, December 2014. arXiv
Conference version: (Informal publication only, details to appear elsewhere)
EuroCG 2014: 30th European Workshop on Computational Geometry
Collection of abstracts, http://www.cs.bgu.ac.il/~eurocg14/accepted.html, 2014, paper 32.
EuroCG website
Efficient algorithms to decide tightness (with Bhaskar Bagchi, Basudeb Datta, Nitin Singh and Jonathan Spreer)
SoCG 2016: 32nd International Symposium on Computational Geometry
To appear, arXiv:1412.1547, December 2014.
arXiv
The cusped hyperbolic census is complete
Transactions of the American Mathematical Society, to appear, arXiv:1405.2695, May 2014.
arXiv
Combinatorial Seifert fibred spaces with transitive cyclic automorphism group (with Jonathan Spreer)
Israel Journal of Mathematics, to appear, arXiv:1404.3005, April 2014.
arXiv
A fast branching algorithm for unknot recognition with experimental polynomial-time behaviour (with Melih Ozlen)
Mathematical Programming, to appear, arXiv:1211.1079, November 2012.
arXiv
Published
Parameterized complexity of discrete Morse theory (with Thomas Lewiner, João Paixão, and Jonathan Spreer)
Journal version: ACM Transactions on Mathematical Software 42:1 (2016), pp. 6:1–6:24. Publisher
Conference version: SCG ’13: Proceedings of the 29th Annual Symposium on Computational Geometry
ACM, 2013, pp. 127–136.
Publisher
2-manifold recognition is in logspace (with Murray Elder, Arkadius Kalka and Stephan Tillmann)
Journal of Computational Geometry 7:1 (2016), pp. 70–85.
Publisher
Tabulation of 3-manifolds of lengths up to 10 (with Akio Kawauchi and Ikuo Tayama)
Topology and its Applications 196 (2015), pp. 937–975.
Publisher
Separation index of graphs and stacked 2-spheres (with Basudeb Datta, Nitin Singh and Jonathan Spreer)
Journal of Combinatorial Theory, Series A 136 (2015), pp. 184–197.
Publisher
arXiv
Algorithms and complexity for Turaev-Viro invariants (with Clément Maria and Jonathan Spreer)
ICALP 2015: Automata, Languages, and Programming: 42nd International Colloquium
Lecture Notes in Computer Science, vol. 9134, Springer, 2015, pp. 281–293.
Publisher
An edge-based framework for enumerating 3-manifold triangulations (with William Pettersson)
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
A new approach to crushing 3-manifold triangulations
Journal version: Discrete and Computational Geometry 52:1 (2014), pp. 116–139. Publisher
Self-archive
Conference version: SCG ’13: Proceedings of the 29th Annual Symposium on Computational Geometry
ACM, 2013, pp. 415–424.
Publisher
Self-archive
A duplicate pair in the SnapPea census
Experimental Mathematics 23:2 (2014), pp. 170–173.
Publisher
Self-archive
Multi-objective integer programming: An improved recursive algorithm (with Melih Ozlen and Cameron A.G. MacRae)
Journal of Optimization Theory and Applications 160:2 (2014), pp. 470–482.
Publisher
arXiv
Fixed parameter tractable algorithms in combinatorial topology (with William Pettersson)
COCOON 2014: Computing and Combinatorics: 20th Annual International Conference
Lecture Notes in Computer Science, vol. 8591, Springer, 2014, pp. 300–311.
Publisher
Self-archive
Enumerating fundamental normal surfaces: Algorithms, experiments and invariants
ALENEX 2014: Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments
SIAM, 2014, pp. 112–124.
Publisher
Self-archive
Locating regions in a sequence under density constraints (with Mathias Hiron)
SIAM Journal on Computing 42:3 (2013), pp. 1201–1215.
Publisher
Self-archive
Optimising a nonlinear utility function in multi-objective integer programming (with Melih Ozlen and Meral Azizoğlu)
Journal of Global Optimization 56:1 (2013), pp. 93–102.
Publisher
Self-archive
A tree traversal algorithm for decision problems in knot theory and 3-manifold topology (with Melih Ozlen)
Journal version: Algorithmica 65:4 (2013), pp. 772–801. Publisher
Self-archive
Conference version: SCG ’11: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry
ACM, 2011, pp. 145–152.
Publisher
Self-archive
Computationally proving triangulated 4-manifolds to be diffeomorphic (with Jonathan Spreer)
(Informal publication only, details to appear elsewhere)
CG:YRF 2013: 29th ACM Symposium on Computational Geometry, Young Researchers Forum
Collection of abstracts, 2013, pp. 15–16.
arXiv
Computing closed essential surfaces in knot complements (with Alexander Coward and Stephan Tillmann)
SCG ’13: Proceedings of the 29th Annual Symposium on Computational Geometry
ACM, 2013, pp. 405–414.
Publisher
Self-archive
The complexity of detecting taut angle structures on triangulations (with Jonathan Spreer)
SODA ’13: Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
SIAM, 2013, pp. 168–183.
Publisher
Self-archive
Computational topology and normal surfaces: Theoretical and experimental complexity bounds (with João Paixão and Jonathan Spreer)
ALENEX 2013: Proceedings of the Meeting on Algorithm Engineering & Experiments
SIAM, 2013, pp. 78–87.
Publisher
Self-archive
Computational topology with Regina: Algorithms, heuristics and implementations
Geometry and Topology Down Under
Contemporary Mathematics, vol. 597, American Mathematical Society, 2013, pp. 195–224.
Publisher
Self-archive
Triangulating a Cappell-Shaneson knot complement (with Ryan Budney and Jonathan Hillman)
Mathematical Research Letters 19:5 (2012), pp. 1117–1126.
Publisher
Pachner moves, generic complexity, and randomising 3-manifold triangulations
(Invited but not reviewed)
Oberwolfach Reports 9:2 (2012), pp. 1412–1414.
Publisher
Self-archive
Computing the crosscap number of a knot using integer programming and normal surfaces (with Melih Ozlen)
ACM Transactions on Mathematical Software 39:1 (2012), pp. 4:1–4:18.
Publisher
Self-archive
The Weber-Seifert dodecahedral space is non-Haken (with J. Hyam Rubinstein and Stephan Tillmann)
Transactions of the American Mathematical Society 364:2 (2012), pp. 911–932.
Publisher
Self-archive
Complementary vertices and adjacency testing in polytopes
COCOON 2012: Computing and Combinatorics: 18th Annual International Conference
Lecture Notes in Computer Science, vol. 7434, Springer, 2012, pp. 507–518.
Publisher
Self-archive
Using Regina to experiment and compute with 3-manifold triangulations and normal surfaces
(Invited but not reviewed)
GTS 2012: Minisymposium on Publicly Available Geometric/Topological Software
Book of abstracts, http://gts2012.tem.uoc.gr/, 2012, pp. 13–18.
GTS website
Self-archive
Maximal admissible faces and asymptotic bounds for the normal surface solution space
Journal of Combinatorial Theory, Series A 118:4 (2011), pp. 1410–1435.
Publisher
Self-archive
Searching a bitstream in linear time for the longest substring of any given density
Algorithmica 61:3 (2011), pp. 555–579.
Publisher
Self-archive
Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations
ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation
ACM, 2011, pp. 59–66.
Publisher
Self-archive
Quadrilateral-octagon coordinates for almost normal surfaces
Experimental Mathematics 19:3 (2010), pp. 285–315.
Publisher
Self-archive
Optimizing the double description method for normal surface enumeration
Mathematics of Computation 79:269 (2010), pp. 453–484.
Publisher
Self-archive
Encouraging algorithmic thinking without a computer
Olympiads in Informatics 4 (2010), pp. 3–14.
Publisher
Self-archive
Get involved! The IOI workshop 2010, its goals and results (with Wolfgang Pohl, Valentina Dagienė, Jittat Fakcharoenphol, Michal Forišek, Mathias Hiron, Mārtiņš Opmanis, Bronius Skūpas, and Willem van der Vegt)
Olympiads in Informatics 4 (2010), pp. 158–169.
Publisher
A mathematician reflecting on the International Olympiad in Informatics
(Non-reviewed publication)
Australian Mathematical Society Gazette 37:1 (2010), pp. 15–21.
Publisher
Self-archive
The complexity of the normal surface solution space
SCG ’10: Proceedings of the Twenty-Sixth Annual Symposium on Computational Geometry
ACM, 2010, pp. 201–209.
Publisher
Self-archive
Converting between quadrilateral and standard solution sets in normal surface theory
Algebraic & Geometric Topology 9:4 (2009), pp. 2121–2174.
Publisher
Self-archive
Breaking the routine: Events to complement informatics olympiad training
Olympiads in Informatics 2 (2008), pp. 5–15.
Publisher
Self-archive
Creating informatics olympiad tasks: Exploring the black art (with Mathias Hiron)
Olympiads in Informatics 2 (2008), pp. 16–36.
Publisher
Self-archive
Informatics olympiads: Challenges in programming and algorithm design
ACSC 2008: Thirty-First Australasian Computer Science Conference
CRPIT, vol. 74, ACS, 2008, pp. 9–13.
Publisher
Self-archive
Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find
Discrete and Computational Geometry 38:3 (2007), pp. 527–571.
Publisher
Self-archive
Observations from the 8-tetrahedron nonorientable census
Experimental Mathematics 16:2 (2007), pp. 129–144.
Publisher
Self-archive
Structures of small closed non-orientable 3-manifold triangulations
Journal of Knot Theory and Its Ramifications 16:5 (2007), pp. 545–574.
Publisher
Self-archive
Informatics olympiads: Approaching mathematics through code
Mathematics Competitions 20:2 (2007), pp. 29–51.
Publisher
Self-archive
Secure group communication with distributed generation of private keys for ad-hoc networks (with Shrikant Sundaram and Peter Bertok)
SEC 2005: Security and Privacy in the Age of Ubiquitous Computing
IFIP Advances in Information and Communication Technology, vol. 181, Springer, 2005, pp. 477–492.
Publisher
Face pairing graphs and 3-manifold enumeration
Journal of Knot Theory and Its Ramifications 13:8 (2004), pp. 1057–1101.
Publisher
Self-archive
Introducing Regina, the 3-manifold topology software
Experimental Mathematics 13:3 (2004), pp. 267–272.
Publisher
Self-archive
Efficient enumeration of 3-manifold triangulations
Australian Mathematical Society Gazette 31:2 (2004), pp. 108–114.
Publisher
Self-archive
Theses
Minimal triangulations and normal surfaces
PhD thesis, The University of Melbourne, 2003.
Self-archive
Completion of partial latin squares
Honours thesis, The University of Queensland, 1996.
Self-archive

(Back to home page...)