Abstract
Let S be a set of m convex polygons in the plane with a total number of n vertices. Each polygon has a positive weight. This paper presents algorithms to solve the weighted minmax approximation and the weighted minsum approximation problems. For the first problem, a line minimizing the maximum weighted distance to the polygons can be found in O(n 2 log n) time and O(n2) space. The time and space complexities can be reduced to O(n log n) and O(n), respectively, when the weights are equal. For the second problem, a line minimizing the sum of the weighted distances to the polygons can be found in O(n2 log n) time and O(n) space. For both problems, we also obtain similar results for sets of n circles or line segments.
This work was done while this author was at McGill University.
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© 1992 Springer-Verlag Berlin Heidelberg
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Robert, JM., Toussaint, G. (1992). Linear approximation of simple objects. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_187
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DOI: https://doi.org/10.1007/3-540-55210-3_187
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