Summary
We reconsider two geometrical problems that have been solved previously by line-sweep algorithms: the measure problem and the contour problem. Both problems involve determining some property of the union of a set of rectangles, namely the size and the contour (boundary) of the union. We devise essentially a single time-optimal divide-and-conquer algorithm to solve both problems. This can be seen as a step towards comparing the power of the line-sweep and the divide-and-conquer paradigms. The surprisingly efficient divide-and-conquer algorithm is obtained by using a new technique called “separational representation”, which extends the applicability of divide-and-conquer to orthogonal planar objects.
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This work was partially supported by the DAAD (Deutscher Akademischer Austauschdienst) and by the DFG (Deutsche Forschungsgemeinschaft)
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Güting, R.H. Optimal divide-and-conquer to compute measure and contour for a set of iso-rectangles. Acta Informatica 21, 271–291 (1984). https://doi.org/10.1007/BF00264251
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DOI: https://doi.org/10.1007/BF00264251