The computational complexity of classical knot recognition-Reference-Cited by-同舟云学术

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The computational complexity of classical knot recognition

Published:2023-10-10 Issue:11 Volume:32 Page:
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Ichihara Kazuhiro¹^ORCID,Nishimura Yuya²^ORCID,Tani Seiichi³^ORCID

Affiliation:

1. Department of Mathematics, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-Ku, Tokyo 156-8550, Japan

2. Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima, 739-8526, Japan

3. Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-Ku, Tokyo 156-8550, Japan

Abstract

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216523500694

Reference19 articles.

1. Introducing Regina, The 3-Manifold Topology Software

2. Converting between quadrilateral and standard solution sets in normal surface theory

3. Optimizing the double description method for normal surface enumeration

4. The complexity of the normal surface solution space

5. Computational Topology with Regina: Algorithms, Heuristics and Implementations

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