Abstract
We study the problem of encoding homotopy of simple paths in the plane. We show that the homotopy of a simple path with k edges in the presence of n obstacles can be encoded using O(n log(n + k)) bits. The bound is tight if k=Ω(n 1 + ε). We present an efficient algorithm for encoding the homotopy of a path. The algorithm can be applied to find homotopic paths among a set of simple paths. We show that the homotopy of a general (not necessary simple) path can be encoded using O(k logn) bits. The bound is tight. The code is based on a homotopic minimum-link path and we present output-sensitive algorithms for computing a path and the code.
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Bespamyatnikh, S. (2004). Encoding Homotopy of Paths in the Plane. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_37
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DOI: https://doi.org/10.1007/978-3-540-24698-5_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21258-4
Online ISBN: 978-3-540-24698-5
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