Low complexity algorithms in knot theory

Olga Kharlampovich; Alina Vdovina

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arXiv · 1803.04908

Low complexity algorithms in knot theory

Olga Kharlampovich·Alina Vdovina

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Abstract

We show that the genus problem for alternating knots with $n$ crossings has linear time complexity and is in Logspace$(n)$. Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We show that the genus problem for these knots belongs to $TC^0$ circuit complexity class. We also show, that the equivalence problem for such knots with $n$ crossings has time complexity $n\log (n)$ and is in Logspace$(n)$ and $TC^{0}$ complexity classes.

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BibTeX RIS

Olga Kharlampovich, Alina Vdovina. 2018-03-13. Low complexity algorithms in knot theory. https://arxiv.org/abs/1803.04908

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