Encoding Homotopy of Paths in the Plane

  • Sergei Bespamyatnikh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sergei Bespamyatnikh
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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