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• W2407677664 startingPage "1646" @default.
• W2407677664 abstract "Almost exactly 100 years ago, Max Dehn described the first combinatorial algorithm to determine whether two given cycles on a compact surface are homotopic, meaning one cycle can be continuously deformed into the other without leaving the surface. We describe a simple variant of Dehn's algorithm that runs in linear time, with no hidden dependence on the genus of the surface. Specifically, given two closed vertex-edge walks of length at most e in a combinatorial surface of complexity n, our algorithm determines whether the walks are homotopic in O(n + e) time. Our algorithm simplifies and corrects a similar algorithm of Dey and Guha [JCSS 1999] and simplifies the more recent algorithm of Lazarus and Rivaud [FOCS 2012], who identified a subtle flaw in Dey and Guha's results. Our algorithm combines components of these earlier algorithms, classical results in small cancellation theory by Gersten and Short [Inventiones 1990], and simple run-length encoding." @default.
• W2407677664 created "2016-06-24" @default.
• W2407677664 creator A5042187195 @default.
• W2407677664 creator A5090023592 @default.
• W2407677664 date "2013-01-06" @default.
• W2407677664 modified "2023-10-17" @default.
• W2407677664 title "Transforming curves on surfaces redux" @default.
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• W2407677664 doi "https://doi.org/10.5555/2627817.2627935" @default.
• W2407677664 hasPublicationYear "2013" @default.
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