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COMGEO
2004
ACM

On simplifying dot maps

10 years 6 months ago
On simplifying dot maps
Dot maps--drawings of point sets--are a well known cartographic method to visualize density functions over an area. We study the problem of simplifying a given dot map: given a set P of points in the plane, we want to compute a smaller set Q of points whose distribution approximates the distribution of the original set P. We formalize this using the concept of -approximations, and we give efficient algorithms for computing the approximation error of a set Q of m points with respect to a set P of n points (with m n) for certain families of ranges, namely unit squares, arbitrary squares, and arbitrary rectangles. If the family R of ranges is the family of all possible unit squares, then we compute the approximation error of Q with respect to P in O(n log n) time. If R is the family of all possible rectangles, we present an O(mn log n) time algorithm. If R is the family of all possible squares, then we present a simple O(m2 n + n log n) algorithm and an O(n2 n log n) time algorithm which...
Mark de Berg, Prosenjit Bose, Otfried Cheong, Pat
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMGEO
Authors Mark de Berg, Prosenjit Bose, Otfried Cheong, Pat Morin
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