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On the complexity of optimal homotopies
[chapter]

2018
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Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
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In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves γ 1 and γ 2 on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between γ 1 and γ 2 where the length of the longest intermediate curve is minimized. Such optimal homotopies

doi:10.1137/1.9781611975031.73
dblp:conf/soda/ChambersMO18
fatcat:bv4n5epbm5dcfiv2t6xhhlu7eq