Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)
Benjamin A. Burton and Finn Thompson. Effective Computation of the Heegaard Genus of 3-Manifolds. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{burton_et_al:LIPIcs.SoCG.2024.30, author = {Burton, Benjamin A. and Thompson, Finn}, title = {{Effective Computation of the Heegaard Genus of 3-Manifolds}}, booktitle = {40th International Symposium on Computational Geometry (SoCG 2024)}, pages = {30:1--30:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-316-4}, ISSN = {1868-8969}, year = {2024}, volume = {293}, editor = {Mulzer, Wolfgang and Phillips, Jeff M.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.30}, URN = {urn:nbn:de:0030-drops-199750}, doi = {10.4230/LIPIcs.SoCG.2024.30}, annote = {Keywords: 3-manifolds, triangulations, normal surfaces, computational topology, Heegaard genus} }
Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)
Benjamin A. Burton and Alexander He. Finding Large Counterexamples by Selectively Exploring the Pachner Graph. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{burton_et_al:LIPIcs.SoCG.2023.21, author = {Burton, Benjamin A. and He, Alexander}, title = {{Finding Large Counterexamples by Selectively Exploring the Pachner Graph}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {21:1--21:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-273-0}, ISSN = {1868-8969}, year = {2023}, volume = {258}, editor = {Chambers, Erin W. and Gudmundsson, Joachim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.21}, URN = {urn:nbn:de:0030-drops-178712}, doi = {10.4230/LIPIcs.SoCG.2023.21}, annote = {Keywords: Computational topology, 3-manifolds, Triangulations, Counterexamples, Heuristics, Implementation, Pachner moves, Bistellar flips} }
Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)
Benjamin A. Burton. The Next 350 Million Knots. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{burton:LIPIcs.SoCG.2020.25, author = {Burton, Benjamin A.}, title = {{The Next 350 Million Knots}}, booktitle = {36th International Symposium on Computational Geometry (SoCG 2020)}, pages = {25:1--25:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-143-6}, ISSN = {1868-8969}, year = {2020}, volume = {164}, editor = {Cabello, Sergio and Chen, Danny Z.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.25}, URN = {urn:nbn:de:0030-drops-121831}, doi = {10.4230/LIPIcs.SoCG.2020.25}, annote = {Keywords: Computational topology, knots, 3-manifolds, implementation} }
Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)
Benjamin A. Burton. The HOMFLY-PT Polynomial is Fixed-Parameter Tractable. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
@InProceedings{burton:LIPIcs.SoCG.2018.18, author = {Burton, Benjamin A.}, title = {{The HOMFLY-PT Polynomial is Fixed-Parameter Tractable}}, booktitle = {34th International Symposium on Computational Geometry (SoCG 2018)}, pages = {18:1--18:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-066-8}, ISSN = {1868-8969}, year = {2018}, volume = {99}, editor = {Speckmann, Bettina and T\'{o}th, Csaba D.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.18}, URN = {urn:nbn:de:0030-drops-87311}, doi = {10.4230/LIPIcs.SoCG.2018.18}, annote = {Keywords: Knot theory, knot invariants, parameterised complexity} }
Published in: Dagstuhl Reports, Volume 7, Issue 2 (2017)
Benjamin Burton, Maarten Löffler, Carola Wenk, and Erin Moriarty Wolf Chambers. Applications of Topology to the Analysis of 1-Dimensional Objects (Dagstuhl Seminar 17072). In Dagstuhl Reports, Volume 7, Issue 2, pp. 64-88, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@Article{burton_et_al:DagRep.7.2.64, author = {Burton, Benjamin and L\"{o}ffler, Maarten and Wenk, Carola and Wolf Chambers, Erin Moriarty}, title = {{Applications of Topology to the Analysis of 1-Dimensional Objects (Dagstuhl Seminar 17072)}}, pages = {64--88}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2017}, volume = {7}, number = {2}, editor = {Burton, Benjamin and L\"{o}ffler, Maarten and Wenk, Carola and Wolf Chambers, Erin Moriarty}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.2.64}, URN = {urn:nbn:de:0030-drops-73536}, doi = {10.4230/DagRep.7.2.64}, annote = {Keywords: curves, graph drawing, homotopy, knot theory} }
Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)
Benjamin Burton, Erin Chambers, Marc van Kreveld, Wouter Meulemans, Tim Ophelders, and Bettina Speckmann. Computing Optimal Homotopies over a Spiked Plane with Polygonal Boundary. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@InProceedings{burton_et_al:LIPIcs.ESA.2017.23, author = {Burton, Benjamin and Chambers, Erin and van Kreveld, Marc and Meulemans, Wouter and Ophelders, Tim and Speckmann, Bettina}, title = {{Computing Optimal Homotopies over a Spiked Plane with Polygonal Boundary}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, pages = {23:1--23:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.23}, URN = {urn:nbn:de:0030-drops-78630}, doi = {10.4230/LIPIcs.ESA.2017.23}, annote = {Keywords: Fr\'{e}chet distance, polygonal domain, homotopy, geodesic, obstacle} }
Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Benjamin Burton, Sergio Cabello, Stefan Kratsch, and William Pettersson. The Parameterized Complexity of Finding a 2-Sphere in a Simplicial Complex. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
@InProceedings{burton_et_al:LIPIcs.STACS.2017.18, author = {Burton, Benjamin and Cabello, Sergio and Kratsch, Stefan and Pettersson, William}, title = {{The Parameterized Complexity of Finding a 2-Sphere in a Simplicial Complex}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {18:1--18:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.18}, URN = {urn:nbn:de:0030-drops-70156}, doi = {10.4230/LIPIcs.STACS.2017.18}, annote = {Keywords: computational topology, parameterized complexity, simplicial complex} }
Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)
Bhaskar Bagchi, Basudeb Datta, Benjamin A. Burton, Nitin Singh, and Jonathan Spreer. Efficient Algorithms to Decide Tightness. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
@InProceedings{bagchi_et_al:LIPIcs.SoCG.2016.12, author = {Bagchi, Bhaskar and Datta, Basudeb and Burton, Benjamin A. and Singh, Nitin and Spreer, Jonathan}, title = {{Efficient Algorithms to Decide Tightness}}, booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)}, pages = {12:1--12:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-009-5}, ISSN = {1868-8969}, year = {2016}, volume = {51}, editor = {Fekete, S\'{a}ndor and Lubiw, Anna}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.12}, URN = {urn:nbn:de:0030-drops-59040}, doi = {10.4230/LIPIcs.SoCG.2016.12}, annote = {Keywords: discrete geometry and topology, polynomial time algorithms, fixed parameter tractability, tight triangulations, simplicial complexes} }
Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)
Benjamin A. Burton, Arnaud de Mesmay, and Uli Wagner. Finding Non-Orientable Surfaces in 3-Manifolds. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
@InProceedings{burton_et_al:LIPIcs.SoCG.2016.24, author = {Burton, Benjamin A. and de Mesmay, Arnaud and Wagner, Uli}, title = {{Finding Non-Orientable Surfaces in 3-Manifolds}}, booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)}, pages = {24:1--24:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-009-5}, ISSN = {1868-8969}, year = {2016}, volume = {51}, editor = {Fekete, S\'{a}ndor and Lubiw, Anna}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.24}, URN = {urn:nbn:de:0030-drops-59168}, doi = {10.4230/LIPIcs.SoCG.2016.24}, annote = {Keywords: 3-manifold, low-dimensional topology, embedding, non-orientability, normal surfaces} }
Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)
Benjamin A. Burton and William Pettersson. An Edge-Based Framework for Enumerating 3-Manifold Triangulations. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 270-284, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
@InProceedings{burton_et_al:LIPIcs.SOCG.2015.270, author = {Burton, Benjamin A. and Pettersson, William}, title = {{An Edge-Based Framework for Enumerating 3-Manifold Triangulations}}, booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)}, pages = {270--284}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-83-5}, ISSN = {1868-8969}, year = {2015}, volume = {34}, editor = {Arge, Lars and Pach, J\'{a}nos}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.270}, URN = {urn:nbn:de:0030-drops-51485}, doi = {10.4230/LIPIcs.SOCG.2015.270}, annote = {Keywords: triangulations, enumeration, graph theory} }
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