Search Results

Documents authored by He, Alexander

Artifact
Software
DOI: 10.4230/artifacts.23286
AlexHe98/idealedge

Authors: Alexander He

Abstract
Cite as

Alexander He. AlexHe98/idealedge (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@misc{dagstuhl-artifact-23286,
   title = {{AlexHe98/idealedge}}, 
   author = {He, Alexander},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:ebcbe72831246d6d99ed7ff98f3cc00940ed808c;origin=https://github.com/AlexHe98/idealedge;visit=swh:1:snp:0aecbae79b28d96e564539477e07d7c034f15e2a;anchor=swh:1:rev:9025c724d3c0c208f67a3b711a9342810c7d8909}{\texttt{swh:1:dir:ebcbe72831246d6d99ed7ff98f3cc00940ed808c}} (visited on 2025-06-20)},
   url = {https://github.com/AlexHe98/idealedge},
   doi = {10.4230/artifacts.23286},
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.55
A Practical Algorithm for Knot Factorisation

Authors: Alexander He, Eric Sedgwick, and Jonathan Spreer

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We present an algorithm for computing the prime factorisation of a knot, which is practical in the following sense: using Regina, we give an implementation that works well for inputs of reasonable size, including prime knots from the 19-crossing census. The main new ingredient in this work is an object that we call an "edge-ideal triangulation", which is what our algorithm uses to represent knots. As other applications, we give an alternative proof that prime knot recognition is in coNP, and present some new complexity results for triangulations. Beyond knots, our work showcases edge-ideal triangulations as a tool for potential applications in 3-manifold topology.
Cite as

Alexander He, Eric Sedgwick, and Jonathan Spreer. A Practical Algorithm for Knot Factorisation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{he_et_al:LIPIcs.SoCG.2025.55,
  author =	{He, Alexander and Sedgwick, Eric and Spreer, Jonathan},
  title =	{{A Practical Algorithm for Knot Factorisation}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.55},
  URN =		{urn:nbn:de:0030-drops-232075},
  doi =		{10.4230/LIPIcs.SoCG.2025.55},
  annote =	{Keywords: Prime and composite knots, (crushing) normal surfaces, edge-ideal triangulations, co-NP certificate, triangulation complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.21
Finding Large Counterexamples by Selectively Exploring the Pachner Graph

Authors: Benjamin A. Burton and Alexander He

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We often rely on censuses of triangulations to guide our intuition in 3-manifold topology. However, this can lead to misplaced faith in conjectures if the smallest counterexamples are too large to appear in our census. Since the number of triangulations increases super-exponentially with size, there is no way to expand a census beyond relatively small triangulations - the current census only goes up to 10 tetrahedra. Here, we show that it is feasible to search for large and hard-to-find counterexamples by using heuristics to selectively (rather than exhaustively) enumerate triangulations. We use this idea to find counterexamples to three conjectures which ask, for certain 3-manifolds, whether one-vertex triangulations always have a "distinctive" edge that would allow us to recognise the 3-manifold.
Cite as

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)

Copy BibTex To Clipboard

@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}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact