Abstract
We study the well-known problem of approximating a polygonal path P by a coarse one, whose vertices are a subset of the vertices of P. In this problem, for a given error, the goal is to find a path with the minimum number of vertices while preserving the homotopy in presence of a given set of extra points in the plane. We present a heuristic method for homotopy-preserving simplification under any desired measure for general paths. Our algorithm for finding homotopic shortcuts runs in O( mlog(n + m) + nlogn log(nm) + k) time, where k is the number of homotopic shortcuts. Using this method, we obtain an O(n 2 + mlog(n + m) + nlogn log(nm)) time algorithm for simplification under the Hausdorff measure.
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Daneshpajouh, S., Ghodsi, M. (2011). A Heuristic Homotopic Path Simplification Algorithm. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21931-3_11
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DOI: https://doi.org/10.1007/978-3-642-21931-3_11
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