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Results tagged with computational-topology
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user 6094
Computational topology is the study of decidability problems in topology and the algorithms that determine decidability. Examples of area of study include Normal Surface theory and the subproblems of unknot and $S^3$ recognition.
12
votes
Reference on Persistent Homology
This paper was released on the arXiv just this (12Sep2018) morning:
"A Brief History of Persistence."
Jose A. Perea. 2018.
arXiv abstract.
"Persistent homology is currently one of the more w …
- 151k
7
votes
Accepted
What is the state of the art for algorithmic knot simplification?
Here is one piece of software, the Book Knot Simplifier,
by
Maria Andreeva, Ivan Dynnikov, Sergey Koval, Konrad Polthier, and Iskander Taimanov,
largely based on Dynnikov's work:
Here we offer a set …
- 151k
4
votes
Accepted
Computational Topology Paper
Perhaps the paper by Jeff Erickson and Pratik Worah,
"Computing the Shortest Essential Cycle,"
Discrete & Computational Geometry,
Volume 44, Issue 4, December 2010 (PDF link),
might serve your purpose …
- 151k
4
votes
Accepted
Triangulation of the surface determined by sampling two of its cross-sections
This is a problem that has been studied for a long time.
I showed with my students Carol Gitlin and Vinita Subramanian, that there does not always
exist a polyhedron that connects two arbitrary polygo …
- 151k