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- W899056912 abstract "We introduce simple codes and fast visualization tools for knotted structures in molecules and neural networks. Knots, links and more general knotted graphs are studied up to an ambient isotopy in Euclidean 3-space. A knotted graph can be represented by a plane diagram or by an abstract Gauss code. First we recognize in linear time if an abstract Gauss code represents an actual graph embedded in 3-space. Second we design a fast algorithm for drawing any knotted graph in the 3-page book, which is a union of 3 half-planes along their common boundary line. The running time of our drawing algorithm is linear in the length of a Gauss code of a given graph. Three-page embeddings provide simple linear codes of knotted graphs so that the isotopy problem for all graphs in 3-space completely reduces to a word problem in finitely presented semigroups." @default.
- W899056912 created "2016-06-24" @default.
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- W899056912 date "2015-01-01" @default.
- W899056912 modified "2023-09-27" @default.
- W899056912 title "A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages" @default.
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- W899056912 doi "https://doi.org/10.5220/0005259900050016" @default.
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