Talk:Unknotting problem

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Ochiai unknot

The picture of "the Ochiai unknot" is not the unknot that took a long time for a computer to untangle. Ochiai has designed a number of of difficult unknots, and the pictured one is reportedly in his textbook about computational knot theory^[1].

The paper by Andrew, Kavraki, Lydia^[2] (cited in the article) cites the paper by Grzeszczuk, Huang, and Kauffman^[3]. They show their unknot on page 271, figure 10, and it is obviously more complicated. They cite Ochiai's paper^[4], but unfortunately they do not specify which of the three knots it is. It appears to be the knot in figure 3.

I will move the image to unknot and add these citations. I will leave it for later or someone else to verify that figure 3 of Ochiai's paper is the unknot from Grzeszczuk, Huang, and Kauffman and redraw it for Wikipedia. — Preceding unsigned comment added by Kmill (talk • contribs) 21:53, 10 November 2017 (UTC)[reply]

References

^ M. Ochiai, Introduction to knot theory by computer, Makino publisher, 1996
^ Ladd, Andrew M.; Kavraki, Lydia E. (2004), "Motion planning for knot untangling", in Boissonnat, Jean-Daniel; Burdick, Joel; Goldberg, Ken; Hutchinson, Seth, Algorithmic Foundations of Robotics V, Springer Tracts in Advanced Robotics, 7, Springer, pp. 7–23, doi:10.1007/978-3-540-45058-0_2.
^ R. Grzeszczuk, M. Huang, and L. Kauffman. Physically-based stochastic simplification of mathematical knots. IEEE Transactions on Visualization and Computer Graphics, 3(3):262-278, 1997
^ M. Ochiai, “Non-Trivial Projections of the Trivial Knot,” S.M.F. Asterisque, vol. 192, pp. 7-9, 1990.

[1] M. Ochiai, Introduction to knot theory by computer, Makino publisher, 1996

[2] Ladd, Andrew M.; Kavraki, Lydia E. (2004), "Motion planning for knot untangling", in Boissonnat, Jean-Daniel; Burdick, Joel; Goldberg, Ken; Hutchinson, Seth, Algorithmic Foundations of Robotics V, Springer Tracts in Advanced Robotics, 7, Springer, pp. 7–23, doi:10.1007/978-3-540-45058-0_2.

[3] R. Grzeszczuk, M. Huang, and L. Kauffman. Physically-based stochastic simplification of mathematical knots. IEEE Transactions on Visualization and Computer Graphics, 3(3):262-278, 1997

[4] M. Ochiai, “Non-Trivial Projections of the Trivial Knot,” S.M.F. Asterisque, vol. 192, pp. 7-9, 1990.

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