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- W2161738802 abstract "We describe an optimal algorithm to decide if one closed curve on a triangulated 2-manifold can be continuously transformed to another, i.e., if they are homotopic. Our algorithm runs in O(n+k/sub 1/+k/sub 2/) time and space, where closed curves C/sub 1/ and C/sub 2/ of lengths k/sub 1/ and k/sub 2/, resp., on a genus g surface M (g/spl ne/2 if M orientable, and g/spl ne/3,4 if M is non-orientable) are presented as edge-vertex sequences in a triangulation T of size n of M. This also implies an optimal algorithm to decide if a closed curve on a surface can be continuously contracted to a point. Except for three low genus cases, our algorithm completes an investigation into the computational complexity of the two classical problems for surfaces posed by the mathematician Max Dehn at the beginning of this century. However, we make novel applications of methods from modern combinatorial group theory for an approach entirely different from previous ones, and much simpler to implement." @default.
- W2161738802 created "2016-06-24" @default.
- W2161738802 creator A5025354167 @default.
- W2161738802 creator A5055803695 @default.
- W2161738802 date "2002-11-19" @default.
- W2161738802 modified "2023-09-23" @default.
- W2161738802 title "Optimal algorithms for curves on surfaces" @default.
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- W2161738802 doi "https://doi.org/10.1109/sfcs.1995.492482" @default.
- W2161738802 hasPublicationYear "2002" @default.
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